The point-slope form of the equation of the line that passes through (–9, –2) and (1, 3) is y – 3 = 1/2 (x – 1). What is the slope-intercept form of the equation for this line?

Answers

Answer 1

You just have to simplify that point-slope equation in order to get it into slope-intercept:
[tex]y-3= \frac{1}{2} (x-1)[/tex]
[tex]y-3= \frac{1}{2}x- \frac{1}{2} [/tex]
[tex]y= \frac{1}{2} x- \frac{1}{2} +3[/tex]
[tex]y= \frac{1}{2} x- \frac{1}{2} + \frac{6}{2} [/tex]
[tex]y= \frac{1}{2} x+ \frac{5}{2} [/tex]

Answer 2

Answer:

[tex]y=\frac{x}{2}+\frac{5}{2}[/tex]

Step-by-step explanation:

Hello

thanks for asking this question, I think I can help you with this

if you have the point-slope form of the equation of a line, just isolate "y" to find the slope-intercept form

Step 1

[tex]y-3=\frac{1}{2} (x-1)\\\\y-3=\frac{x}{2}-\frac{1}{2} \\Add\ 3\ in\ both sides\\\\y-3+3=\frac{x}{2}-\frac{1}{2} +3\\y=\frac{x}{2}-\frac{1}{2}+3\\y=\frac{x}{2}+\frac{5}{2}[/tex]

so the answer is

[tex]y=\frac{x}{2}+\frac{5}{2}[/tex]

where 1/2 is the slope, and 5/2 is the intercept with y-axis

I really hope it helps , Have a great day.

Related Questions

Which number line represents the solution set for the inequality 2x – 6 ≥ 6(x – 2) + 8?

what way do you shade in

Answers

2x - 6 > = 6(x - 2) + 8...distribute thru the parenthesis
2x - 6 > = 6x - 12 + 8...simplify
2x - 6 > = 6x - 4...subtract 6x from both sides
2x - 6x - 6 > = 6x - 6x - 4...simplify
-4x - 6 > = -4 ...add 6 to both sides
-4x - 6 + 6 > = -4 + 6...simplify
-4x > = 2...divide both sides by -4, change the inequality sign
x < = -2/4
x < = -1/2 or -0.5

so u would have a solid circle (because of ur equal sign) on -1/2...and the shading would go to the left (because less then goes to the left)

** the reason the inequality sign was changed is because when multiplying/dividing by a negative, u have to flip the sign...but dont forget to keep the = sign in there

Answer:

x < = -1/2 or -0.5

Step-by-step explanation:

that's the answer

Solve the system using elimination. y – x = 13 7y + x = 11

Answers

y – x = 13
7y + x = 11
---------------------add
8y = 24
y = 3

y – x = 13
3 – x = 13
-x = 10
x = -10

answer
x = -10 and y = 3

To make bread dough, a baker mixes flour, eggs, yeast and salt by weight in pounds in the ratio of 11:9:3:2, respectively. how many pounds of yeast are required to make 20 pounds of bread dough?

Answers

In a standard batch, you have 11 pounds of flour, 9 pounds of eggs, 3 pounds of yeast and 2 of salt. This means the bread dough will weigh 11+9+3+2=25 pounds. The ratio of yeast to dough is then 3:25. To get 20 pounds of dough, we need x amount of yeast. Since its a ratio, 3/25 = x/20. We then solve for x, so x = 20*(3/25) = 12/5 = 2.4 pounds of yeast.

Which line is parallel to the line y=12x+5 and passes through the point (-2, 1)?

Answers

The equation of the line parallel to y=12x+5 that passes through the point (-2, 1) is y=12x+25.

Since the two lines are parallel, they will have the same slope. The slope of the given line is the coefficient of x, which is 12. Therefore, the line we are looking for also has a slope of 12.

To find the equation of the new line, we'll use the point-slope form of a line equation, which is y - y1 = m(x - x1), where m is the slope and (x1, y1) is the given point.

Substituting the given point and the slope into this form we get:

y - 1 = 12(x + 2)

Expanding and simplifying this, we have:

y - 1 = 12x + 24

Finally, adding 1 to both sides to solve for y, we get:

y = 12x + 25, which is the equation of the line that is parallel to y=12x+5 and passes through the point (-2, 1).

The graph shows the functions f(x), p(x), and g(x): Graph of function g of x is y is equal to 1 plus the quantity 1.5 raised to the power of x. The straight line f of x joins ordered pairs 4, 1 and 2, negative 3 and is extended on both sides. The straight line p of x joins the ordered pairs 0, 2 and 1, negative 5 and is extended on both sides. Courtesy of Texas Instruments Part A: What is the solution to the pair of equations represented by p(x) and f(x)? (3 points) Part B: Write any two solutions for f(x). (3 points) Part C: What is the solution to the equation p(x) = g(x)? Justify your answer. (4 points)

Answers

Part A: Intersection at [tex]$(-13/4, -83/4)$[/tex].

Part B: Two solutions for [tex]$ f(x) $: (0, -11) and (5, 14).[/tex]

Part C: Solve [tex]$ p(x) = g(x) $[/tex] graphically for the Point of intersection

Part A: Solution to the Pair of Equations (p(x) and f(x)):

The solution to the pair of equations represented by [tex]$ p(x) $ and $ f(x) $[/tex]is the point of intersection. From the information provided, it seems that the intersection point is [tex]$(-13/4, -83/4)$.[/tex]

Part B: Two Solutions for [tex]$ f(x) $[/tex]:

1. [tex]$ (0, -11) $[/tex]

2. [tex]$ (5, 14) $[/tex]

Part C: Solution to [tex]$ p(x) = g(x) $[/tex]:

To find the solution to [tex]$ p(x) = g(x) $, set $ p(x) = 7x + 2 $[/tex] equal to [tex]$ g(x) = 1 + 1.5^x $. Solve for $ x $[/tex] to determine the point of intersection between [tex]$ p(x) $ and $ g(x) $[/tex]. The solution to this equation provides the [tex]$ x $[/tex] coordinate, and substituting it into either [tex]$ p(x) $ or $ g(x) $[/tex] gives the [tex]$ y $[/tex] coordinate. The justification lies in the graphical intersection of the functions.

Note: It's essential to examine the graph for precise details, as visual inspection can help confirm the solutions.

For such more questions on point of intersection

https://brainly.com/question/29185601

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the minute hand of a clock is 9.5cm long, How far does the tip of the hand travel in one day?

Answers

The tip of the hand travels the circumference of a circle with radius (r) 9.5 cm every hour;
The formula for circumference of a circle (c) is:
c = πd = 2πr
So, for a circle with radius 9.5, the circumference is:
c = 2π(9.5)
= 19π cm
The tip travels 19π cm every hour, so in a day of 24 hours it will travel:
24 * 19π = 456π cm
(= 1432.566... ⇒ 1432.6 cm)

What is the equation in point-slope form of the line passing through (0, 5) and (−2, 11)? y − 5 = −3(x + 2) y − 5 = 3(x + 2) y − 11 = −3(x − 2) y − 11 = −3(x + 2)

Answers

hello :

Hello : let A(0,5) B(-2,11)
the slope is : (YB - YA)/(XB -XA)
(11-5)/(-2-0) = 6/(-2)
the slope is : -3

the equation in point-slope form of the line is : y-11 = -3(x+2)

Answer: [tex]y-11=-3(x+2)[/tex]

Step-by-step explanation:

Given points : (0, 5) and (−2, 11)

Slope of the line passing through given points .

[tex]m=\frac{y_2-y_1}{x_2-x_1}=\frac{11-5}{-2-0}=\frac{6}{-2}=-3[/tex]

Thus, slope of line passing through given points m=-3

We know that the equation of a line passing through points [tex](x_0,y_0)[/tex] with slope 'm' is [tex](y-y_0)=m(x-x_0)[/tex]

Thus, equation of a line passing through (−2, 11) with slope m=-3 will be

[tex](y-11)=(-3)(x-(-2))\\\Rightarrow\ y-11=-3(x+2)[/tex]

Hence, the equation of line is [tex]y-11=-3(x+2)[/tex]

points (0,0) and (3,3) lie on line k what is the slope of the line that is perpendicular to k

Answers

slope equation: y2-y1 over x2-x1
3-0 over 3-0 = 1
to get the perpendicular slope of a line, you must use the negative reciprocal therefore, the slope of a line that is perpendicular to k is equal to -1

The graph below shows a line segment PQ: graph of line PQ going through ordered pairs negative 1, 3 and 2, negative 3 Which of the following equations best represents the line segment PQ?A: y = −3x + 2B: y = −2x + 1C: y = −3x − 2D: y = −2x − 1

Answers

You actually don't need a graph to be able to solve this equation. As long as you are given two data points, you can already solve for the linear equation.

The most common way of writing linear equations is the slope-intercept form:
y = mx + b, where m is the slope and b is the y-intercept.

The slope is the ratio of the change of y to the change of x coordinates. Let's say point 1 is (-1,3) and point 2 is (2,-3). Then,

m = (-3-3)/(2-⁻1) = -2

Next, we use any of the given point to the standard equation along with the m to find b. Let's use (-1,3)

3 = -2(-1)+b
b = 1

Thus, the complete linear equation is y = -2x + 1. The answer is B.

Answer:

y = -2x + 1. The answer is B.

Step-by-step explanation:

Tony is four years younger than his brother josh, and two years older than his sister cindy. tony also has a twin brother, evan. all the ages of the children totaled together is 66. how old is tony?

Answers

To solve this problem, let us assign the variables. Let us say that:

x = age of Tony = which also the age of his twin brother Evan

x + 4 = age of Josh (since tony is 4 years younger, then josh must be 4 years older)

x – 2 = age of Cindy (since tony is 2 years older, then cindy must be 2 years younger)

There are a total of 4 children, therefore:

x + x + x + 4 + x – 2 = 66

4 x + 2 = 66

4 x = 64

x = 16

Therefore Tony is 16 years old.

Final answer:

To find Tony's age, we can set up an equation using the information given and solve for x. After solving the equation, we find that Tony is 16 years old.

Explanation:

To solve this problem, we can assign variables to each person's age. Let's say Tony is x years old. Since Tony is four years younger than Josh, Josh's age can be represented as x + 4. Since Tony is two years older than Cindy, Cindy's age can be represented as x - 2. Since Tony has a twin brother, Evan, we can assign Evan's age as x as well.

According to the information provided, the sum of all their ages is 66, so we can set up the equation: x + (x + 4) + (x - 2) + x = 66. Simplifying the equation, we get 4x + 2 = 66. By subtracting 2 from both sides and dividing by 4, we find that x = 16.

Therefore, Tony is 16 years old.

State two reasons why including the p-value is prudent when you are reporting the results of a hypothesis test.

Answers

In general as we know when we perform a hypothesis test in statistics then p value help us to determine the significance of our result.
Hypothesis test are generally used to test a validity of claim that is made about a population.This claim that's on trial in essence is called as a Null Hypothesis.

The p - values is a number between 0 to 1 and interpreted in following way:

A small p - value (<= 0.05) indicates the strong evidence against a null hypothesis , so you reject a null hypothesis.

A large p - value (>0.05) indicates weak evidence against a null hypothesis , so you fail to reject the null hypothesis.

The reason which include the p - value is prudent when you are reporting the result of a hypothesis test are given below:

1. It allows us for evaluating the strength of the evidence against the null hypothesis.

2. Allow us for assessing significance at any desired level . The null hypothesis can be rejected at any significance level larger than or equal to p - value and it can not be rejected at any significance level smaller than the p - value.

The length of a rectangle is twice its width. if the area of the rectangle is 162 cm2 , find its perimeter.

Answers

Let the width of the rectangle be x
Then, the length of the rectangle will be 2x
The area of the rectangle will be
2x(x)=2x^2
Since the area of the rectangle is 162cm2
2x^2=162
x^2=81
x=9
Width of the rectangle=9
Length of the rectangle=9x2=18
Perimeter of a rectangle
=2(width) + 2(length)
=2(9)+2(18)
=54cm

The line through the midpoint of and perpendicular to the segment joining points (1, 0) and (5, -2). The answe is x_ _= something

Answers

First, you have to find the midpoint of the segment. Using the midpoint theorem, (which is (x1+x2)/2, (y1+y2)/2 ) the midpoint of that segment in (3,-1)

Next find the slope of the segment 1,0 and 5,-2 using rise over run or deltax / deltay which is a fancy way of saying change in x over change in y.

The slope is 4/2 or 2
When a line is perpendicular to another the slope is the negative reciprocal so the slope of our new line will be -1/2

Now plug in the coordinate (3, -1) to find the y-intercept and the equation of that line will be complete

so -1 = -1/2 (3) +b
-1= -1.5 +b
0.5 = b

The final equation will be -1/2x + 0.5 =y

hope this helps:)

what is the range of f(x)=log0.6x

Answers

The range of a log is all real numbers, only the domain is limited. Therefore the answer is +infinity to -infinity.

Which law would you use to simplify the expression (p/q)^3

Answers

Answer:

B. Power of quotient.

Step-by-step explanation:

We have been given an expression [tex](\frac{p}{q} )^3[/tex] and we are asked to choose the correct rule to simplify our given expression.

Since our given expression is a fraction raised to 3rd power. Power of a quotient rule states when a quotient is raised to an exponent, then the exponent is distributed to both numerator and denominator of the quotient.

Using power of a quotient rule, we will get,

[tex](\frac{p}{q} )^3=\frac{p^3}{q^3}[/tex]

Therefore, we can simplify our given expression using power of a quotient and option B is the correct choice.

The power of quotients is the law that would be used to simplify the expression.

What is the power of quotients?

This is a mathematical rule that states that the power of a quotient is the same thing as the quotient that is gotten.

Given that the numerator p and the denominator q are raised to to the power expressed in the question separately.

The division is calculated after this has done

Read more on the power of quotient here:

https://brainly.com/question/2141690

In the above figure, AE = 2, CE = 3, and DE = 4. What is the length of BE?

Answers

BE= 6. I had this question not too long ago. Hope this helps. :)

Answer:

its 6 i think

Explanation:

if you have the choices 6, 8, 12, 5.. then 6 is ur answer. why?

well u do CE x DE = AE x BE

(3)(4)= (2)(BE)

12=2x

12÷2= 6

Two lines are perpendicular. if one line has a slope of 0, what is the slope of the other line?

Answers

If two lines are perpendicular, then one line is an opposite reciprocal of the other. Since one line has a slope of 0, the opposite reciprocal of 0 would be -0/0, but any number over 0 is described as undefined, so the slope of the other line is undefined.

Describe the graph of the function.y = |x – 4| – 7

Answers

This is always ''interesting'' If you see an absolute value, you always need to deal with when it is zero:

(x-4)=0 ===> x=4,

so that now you have to plot 2 functions!

For x<= 4: what's inside the absolute value (x-4) is negative, right?, then let's make it +, by multiplying by -1:

|x-4| = -(x-4)=4-x
Then:

for x<=4, y = -x+4-7 = -x-3

for x=>4, (x-4) is positive, so no changes:

y= x-4-7 = x-11,

Now plot both lines. Pick up some x that are 4 or less, for y = -x-3, and some points that are 4 or greater, for y=x-11

In fact, only two points are necessary to draw a line, right? So if you want to go full speed, choose:

x=4 and x= 3 for y=-x-3

And just x=5 for y=x-11

The reason is that the absolute value is continuous, so x=4 works for both:

x=4===> y=-4-3 = -7

x==4 ====> y = 4-11=-7!

abs() usually have a cusp int he point where it is =0

Hope it helps, despite being this long!

Answer with explanation:

We are given a function as:

[tex]y=|x-4|-7[/tex]

We know that this function is a transformation of the parent function y=|x| i.e. the modulus function.

The rule that holds in this transformation is:

It is a translation of the parent function 4 units to the right and 7 units down.

Also, the graph of the function is attached to the answer.

Choose the correct simplification of (6x4y2z3)(3x4y3z5).
18x16y6z15
18x8y5z8
9x8y5z8
9x16y6z15

Answers

6x4 * 3x4 = 18x^8

y2*y3 = y5
z3 * z5 = z8

answer is 18x8y5z8

B

Answer:

18 x 8y 5z 8 witch is answer choice B

Step-by-step explanation:

A carpet cleaning business has 100 customers when they charge $125 for a cleaning. Research shows that every $5 reduction in price attracts another 20 customers. What price should the business implement to maximize its revenue?
a $75
b $100
c $120
d $90

Answers

Since a $5 decrease in price increases customers by 20 we can say that we have two points:

(125,100) and (120,120), from these we can find the slope or rate of change of customers as a function of price...

m=20/-5

m=-4

m=-4

c(p)=-4p+b, now we can use (125,100) to solve for b

100=-4(125)+b

100=-500+b

600=b, so our number of customers as a function of price is:

c(p)=600-4p

Revenue will simply be the number of customers times the price charged per customer...or p*c(p):

r(p)=600p-4p^2

We can find price that creates maximum revenue by finding when the derivative is equal to zero...

dr/dp=600-8p

dr/dp=0 only when

0=600-8p

8p=600

p=75

So the price that maximizes revenue is $75.

The linear relationship is c(p) = -4p + b. Then the price that maximizes revenue is $75.

What is the linear system?

It is a system of an equation in which the highest power of the variable is always 1.

A carpet cleaning business has 100 customers when they charge $125 for cleaning.

Research shows that every $5 reduction in price attracts another 20 customers.

Since a $5 decrease in price increases customers by 20, we can say that we have two options.

(120, 100) and (120, 120) from these we can find the slope or rate of change of customers as a function of price.

[tex]\rm m = \dfrac{20}{-5}\\\\ m = -4[/tex]

Then we have

[tex]\rm c(p ) = -4 p +b[/tex]

Now, we can use (125, 100) to solve for b

100 = -4(125) + b

b = 600

So our number of customers as a function of price is

[tex]\rm c(p) = 600 - 4p[/tex]

Revenue will simply be the number of customers times the price charged per customer will be

[tex]\rm r(p) = 600 p -4p^2[/tex]

We can find a price that creates maximum revenue by finding when the derivative is equal to zero.

[tex]\rm \dfrac{dr}{dp} = 600 - 8p\\\\[/tex]

WE know that for maximum,

[tex]\rm \dfrac{dr}{dp} = 0\\\\0 = 600 - 8p\\\\p = 75[/tex]

So, the price that maximizes revenue is $75.

More about the linear system link is given below.

On Mars, if you hit a baseball, the height of the ball at time "t" would be modelled by the quadratic function h=-1.85t^2+20t+1, where t is in seconds and h is in metres. When will the ball hit the ground?

Answers

Given that the height of the baseball is modeled by the equation:
h(t)=-1.85t^2+20t+1
where t is time in seconds and h is the height in meters
The time taken for the ball to hit the ground will be found as follows;
at the point when the ball hits the ground, h(t)=0, therefore our equation will be:
-1.85t^2+20t+1=0
solving the above quadratic equation for t we get:
t=[-b+/-sqrt(b^2-4ac)]/(2a)
substituting the values into the above formula we get:
t=[-20+\-sqrt(20^2+7.4)]/(-3.7)
t=-0.049771
or
t=10.8606
but since there is no negative time values we shall select:
t=10.8606
hence, we conclude that the time taken for the ball to hit the ground was:
t=10.8606 seconds

Which person in the high rise building is closest to the street level?Moira is in her doctor’s office on the fourth floor.Geoffrey is in the elevator between the second and third floors.Sandy is in the laundry room on the –2 basement floor.Hasim is leaving the parking garage and is currently between –1 and –2 levels.

Answers

Arranging in value from top to bottom. The chart is Moira (4), Geoffrey (2.5) Ground Floor (0), Hasim (-1.5) and Sandy (-2). The closest number to 0 is -1.5, so that means that Hasim is the closest to the ground floor.

Answer

Hasim is the closest... I just took the test

Write an inequality for the situation.

all real numbers y that are less than –3 or greater than 18

A) y < –3 or y < 18
B) y < 18 or y > –3
C) –3 < y < 18
D) y < –3 or y > 18

Answers

The answer is D. The numbers for y have to be less than -3, which is shown using the less than sign, and they also have to be greater than 18, which is shown with the greater than sign.

All real numbers y that are less than -3 means that the values of y need to be less than -3 so;
y<-3.
Next, it is greater than 18 which means the value of y is greater than 18;
y>18
Also, this is known as the compound inequality which you could write as: 1818. In conclusion, D is the only correct answer. Have a nice day!

What are the possible values of x in x2 + 3x + 3 = 0?

Answers

I'm assuming that that is a quadratic equation:
[tex] x^{2} +3x+3=0[/tex]
The only way to solve this is to use the quadratic formula. When you do that you get a negative number under the square root sign which we all know is illegal, UNLESS you factor out the imaginary "i". So your roots would be this:
[tex]x= \frac{-3+ \sqrt{3}i }{2} ,x= \frac{-3- \sqrt{3}i }{2} [/tex]

Find the value of X.

Answers

RS + ST = RT

3x + 1 + 2x - 2 = 64
5x - 1 = 64
5x = 64 + 1
5x = 65
x = 65/5
x = 13 <==

Solve by taking square roots: x^2 - 40 = 9

Answers

To solve for x^2 - 40 = 9, take the square roots of both sides and solve.
The answer is x = 7, -7.

[tex] x^{2} -40= 9[/tex]

[tex] x^{2} = 49[/tex]

[tex] \sqrt{ x^{2} } = \sqrt{49} [/tex]

x = +7 or -7

Compare 9 ⋅ 104 to 3 ⋅ 102.

9 ⋅ 104 is 3 times larger than 3 ⋅ 102.
9 ⋅ 104 is 30 times larger than 3 ⋅ 102.
9 ⋅ 104 is 300 times larger than 3 ⋅ 102.
9 ⋅ 104 is 3,000 times larger than 3 ⋅ 102.

Answers

9×10⁴ is 300 times greater than 3×10²
as, (9×10⁴)/(3×10²)=3× 10²
and the proper of writting powers in computer form is a×10^b

Answer:

9×10⁴ is 300 times greater than 3×10²

Step-by-step explanation:

guy above me's work. thanks to him we get this answer :)

What is the remainder of (x3 - 6x2 - 9x + 3) ÷ (x - 3) A. -25 B. -52 C. -51 D. -17

Answers

D is the correct answer.

BRAINLIEST PLS!!!

the correct answer in C. -51 hope this helps you

2, -4, 8, -16, . . . find the next two numbers in the pattern and describe the pattern.

Answers

the next numbers are 32 and -64 the pattern multiplies by -2

If the tangent line to y = f(x) at (7, 4) passes through the point (0, 3), find f(7) and f '(7).

Answers

hello :
f'(7) = the slope of the tangent line : let A(7,4) B(0,3)
the slope is : (YB - YA)/(XB -XA)= (3-4)/(0-7) = -1/-7 = 1/7=f'(7)
the equation of the tangent line is :
y-3 = 1/7 (x-0)
y = (1/7)x+3
the line tangent and the graph of : f passes through the point A(7, 4)
x= 7 y=4 so : f(7) =4

Final answer:

To find f(7) and f'(7) of y = f(x) given a point on the tangent line passing through another point.

Explanation:

Given:
Equation of tangent line to y = f(x) at (7, 4) passes through (0, 3).
To find:
f(7) and f'(7).

Find slope of tangent line using the two points: m = (3-4)/(0-7) = 1/7.Since slope of tangent = f'(7), f'(7) = 1/7.Using the point (7, 4) and slope 1/7, find the equation of the tangent line: y - 4 = (1/7)(x - 7).Substitute x = 7 in the equation to find f(7), which results in f(7) = 4.

Other Questions

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