A linear function F models a relationship in which the dependent variable decreases 6 units for every 3 units the independent variable decreases. The value of the function at 0 is 4. Graph the function. Identify the slope, y-intercept, and x-intercept of the graph.
Answers
A. Finding the slope
The slope of the function is simply the ratio of the value of the dependent variable over the independent variable, so in this case it is:
slope = 6/ 3 = 2
B. Finding the y – intercept
The y – intercept is simply the value of the dependent variable when the independent variable is equal to zero, therefore:
y – intercept (b) = 4
C. Finding the function of the graph
The general equation of a line is given as:
y = m x + b
where m is the slope and b is the y intercept therefore:
y = 2 x + 4
D. Finding the x – intercept
The x – intercept is simply the value of the independent variable (x) when the dependent variable (y) is equal to zero, therefore:
0 = 2 x + 4
x = - 2
E. Graph the function
Check out the image attached
The linear function described is y = -2x + 4, with a slope of -2 and a y-intercept at (0,4). The line for this function will pass through the points (0,4) and (2,0), the latter being the x-intercept.
Explanation:The question asks to graph a linear function in which the dependent variable decreases 6 units for every 3 units the independent variable decreases, and the function's value at 0 is 4. The nature of this relationship implies that the slope of this function is -2 (calculated as -6 divided by 3). Therefore, the equation for this linear function, using the slope-intercept form y = mx + b, will be y = -2x + 4. In this equation, -2 is the slope (m) and 4 is the y-intercept (b, the function's value when x is 0).
To graph this function, you start by marking the point (0,4) on your graph. From this point, you then go down 2 units (as the slope is -2) and 1 unit to the right (as the decrease in y for a 1 unit increase in x). You will continue this pattern to graph the line. The x-intercept—the point at which the line crosses the x-axis (i.e., where y = 0)—occurs at x = 2, because plugging in 0 for y in the equation gives us -2x + 4 = 0, which simplifies to x = 2. So the final line should pass through the points (0,4) and (2,0).
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Related Questions
Product a is an 8 oz bottle of cough medication that sells for a $1.36 product B is a 16oz bottle of cough medication that costs $3.20 which product has the lower unit price
Answers
3.20 ÷ 16 = 0.2
Product B has a lower unit price (dollar per ounce)
URGENT WILL MARK BRAINLIEST!
Starting at sea level, a submarine descended at a constant rate to a depth of −4/5 mile relative to sea level in 3 minutes.
What was the submarine's depth relative to sea level after the first minute?
Simplest form please!
Answers
I believe the correct answer is -4/15.
Hope this helps! ☺♥
i hoped this helps
To graph the equation 2x + 5y = 10, Zeplyn draws a line through the points (5, 0) and (0, 2). What is the slope of the line represented by 2x + 5y = 10?
Answers
It's B
just took test
The equation of the line passing through points (5, 0) and (0, 2) is y = -2/5x + 2 and slope is -2/5.
What is Slope of Line?The slope of the line is the ratio of the rise to the run, or rise divided by the run. It describes the steepness of line in the coordinate plane.
The slope intercept form of a line is y=mx+b, where m is slope and b is the y intercept.
The slope of line passing through two points (x₁, y₁) and (x₂, y₂) is
m=y₂-y₁/x₂-x₁
The given equation is 2x + 5y = 10.
We have to change this equation to slope intercept form
Isolate the term y from the equation
Subtract 2x from both sides
5y = -2x + 10
Divide both sides by 5
y = -2/5x + 2
the slope will be -2/5
Hence, the equation of the line passing through points (5, 0) and (0, 2) is y = -2/5x + 2 and slope is -2/5.
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Show me one way to count from $82 to $512
Answers
This scenario is useful because it can help you count 82 from 512 by breaking up the number. Doing so prevents you from over thinking the problem, etc.
3. The three salespeople for a local advertising firm are Lola, Ahmed, and Tommy. Lola sold $2030 in ads, Ahmed sold $1540, and Tommy sold $1800.
(a) What fraction of the total sales did each salesperson sell?
(b) A $100 bonus was awarded to the three salespeople, which they had to share. It was awarded so that each salesperson received the same fraction of $100 as he or she sold of the total sales. How much did each person receive? Round to the nearest
answer a and b
Answers
Add the three totals.
Total sales for all three: $2030 + $1540 + $1800 = $5370
Now divide each person's sales by the total sales to find each person's fraction of the sales.
Lola: 2030/5370
Ahmed: 1540/5370
Tommy: 1800/5370
3. (b)
Multiply each fraction from part (a) by $100.
Lola: 2030/5370 * $100 = $37.80
Ahmed: 1540/5370 = $28.67
Tommy: 1800/5370 = $33.52
81 is 54% of what number
Answers
54X / 100 = 81/1
crossmultiply
54x = 8100
x= 150
Hope this helped! :)
Hope it helps :)
which two square roots are used to estimate 47
Answers
The two square roots used to estimate the number 47 are 6 and 7, because their squares, 36 and 49 respectively, are the nearest perfect squares to 47.
Explanation:The problem is asking for the two square roots used to estimate the number 47. To solve this, think of two perfect squares that are the closest to 47. Those would be the squares of 6 and 7, because 62 equals 36 and 72 equals 49, which are the closest perfect squares to 47. So, we would use 6 and 7 to estimate the square root of 47.
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Please figure this out and show your work
Answers
(7-b)+(3b+2)
Steps:
Simplify
7-b+3b+2
= 7+-b+3b+2
Combine like terms
=7+-b+3b+2
= (-b+3b)+(7+2)
= (-b+3b) + (7+2)
2b+9
Hope I did it right ^.^
Solve for x, show all your work:
x3 = 10
Answers
repeating
Which word completely describes the rhombus?
A.equilateral
B.equiangular
C.regular
Answers
A sweater is marked down $25 to $19 what is the percent of change
Answers
Cross multiply:
1,900
Divide 1,900 by 25
Equals 76
Subtract 76 from 100
Answer: 24% change
I hope this helps!
To solve the problem we must know about Percentage.
PercentageA percentage is a way to describe a part of a whole. such as the fraction [tex]\bold{\dfrac{1}{4}}[/tex] can be described as 0.25 which is equal to 25%.
To convert a fraction to a percentage, convert the fraction to decimal form and then multiply by 100 with the '%' symbol.
Given to us
A sweater is marked down $25 to $19AssumptionLet the x% be the remaining amount.
Remaining Amountx% of $25 = $19
[tex]\dfrac{x}{100} \times \$25 = \$19\\\\\dfrac{x}{100} \times 25 = 19\\\\\dfrac{x}{4} = 19\\\\x = 19\times 4\\x = 76[/tex]
Thus, $19 is 76% of $25.
Percent of changethe percent of change = Orignal percentage - final percentage
= 100% - 76%
= 24%
Hence, the percentage change is 24%.
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What is the slope-intercept form of the linear equation 2x–8y=32 ?
What is the equation of this graphed line?
Enter your answer in slope-intercept form in the box. (Graph is on picture)
Which equation shows y=3/4x-5/2 in standard form?
A. 3x−4y=10
B. 3x−4y=−10
C. 4x−3y=10
D. 4x−3y=−10
Answers
1. The slope-intercept form of the linear equation [tex]\(2x - 8y = 32\)[/tex] is [tex]\(y = \frac{1}{4}x - 4\).[/tex]
2. The equation of the graphed line is [tex]\(y = -\frac{9}{8}x + 7\).[/tex]
3. The standard form of [tex]\(y = \frac{3}{4}x - \frac{5}{2}\)[/tex] is option A: [tex]\(3x - 4y = 10\).[/tex]
Let's break down the given information step by step:
1. Slope-Intercept Form of the Linear Equation:
- The given equation is 2x - 8y = 32.
- To express it in slope-intercept form (y = mx + b), we need to solve for y:
2x - 8y = 32
-8y = -2x + 32
[tex]y = \frac{1}{4}x - 4[/tex]
Therefore, the slope-intercept form of the given equation is [tex]\(y = \frac{1}{4}x - 4\)[/tex].
2. Equation of the Graphed Line:
- The graphed line has the equation [tex]\(y = -\frac{9}{8}x + 7\)[/tex].
3. Standard Form of [tex]\(y = \frac{3}{4}x - \frac{5}{2}\)[/tex]:
- We want to express [tex]\(y = \frac{3}{4}x - \frac{5}{2}\)[/tex] in standard form (Ax + By = C).
- Multiply both sides of the equation by 4 to get rid of fractions:
4y = 3x - 10
3x - 4y = 10
Therefore, the standard form of [tex]\(y = \frac{3}{4}x - \frac{5}{2}\) is \(3x - 4y = 10\)[/tex].
Given this information, the correct answer is A. 3x − 4y = 10.
Modeling with systems of linear inequalities
Answers
Modeling with systems of linear inequalities involves using multiple linear inequalities to represent constraints and solve problems with multiple variables. We can graph the inequalities on a coordinate plane and find the feasible region, which represents all the solutions that satisfy the constraints.
Explanation:Modeling with systems of linear inequalitiesModeling with systems of linear inequalities is a mathematical concept that involves using multiple linear inequalities to represent constraints in a real-world situation. This allows us to model and solve problems involving multiple variables and constraints, such as optimizing profit or finding feasible solutions.
Here's an example:
Let's say we have two variables, x and y, representing the number of units of two products.We also have two inequalities, 2x + 3y <= 10 and x + y >= 4.These inequalities represent constraints on the production and sales of the products.To model this situation, we graph the two inequalities on a coordinate plane.The feasible region, the area where the shaded regions of both inequalities overlap, represents the set of solutions that satisfy all the constraints.We can then use this model to analyze and solve various problems, such as finding the maximum profit by maximizing a certain objective function within the feasible region.Learn more about Modeling with systems of linear inequalities here:https://brainly.com/question/34246005
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What is the factored of the expressions 3×2+8×-16
Answers
So 3*2=6 and 8*-16 is -128, then you add them both.
So 6+(-128) is equals to -122. YOU'RE WELCOME :D
(c) Mrs. Dewalt looked at another hotel. She waited a week before she decided to book nights at that hotel, and now the prices have increased. The original price was $1195. The price for the same room and same number of nights is now $2075. What is the percent increase? Round to the nearest whole percent. Explain and Show your work.
Answers
Hope This Helps!
Hope it helped!
Mate weighed each of his cats. He found that Betty weighed 1 1/4 kilograms, Fido weighed 2 kilograms, Spot weighed 1 5/8 kilograms, Yogi weighted 3 4/9 kilograms, and Smart weighed 4 1/10 kilograms
What was the weight of Nate’s heaviest cat?
Answers
The weight of Nate’s heaviest cat is:
4 1/10 kilograms=4.1 kilograms ( Smart)
Step-by-step explanation:Weight of Betty is:1 1/4 kilograms which in decimals is: 1.25 kilograms.
Also,
Weight of Fido is:2 kilograms
Weight of Spot is:1 5/8 kilograms which in decimals is: 1.625 kilograms
Weight of Yogi is:3 4/9 kilograms which in decimals is: 3.444 kilograms
Weight of Smart is:4 1/10 kilograms which in decimals is: 4.1 kilograms
Hence, we observe that Smart weight is highest amongst the weight of the other cats.
Set up the equation
The product of a number(variable) and 4 increased by 16 is -2
Answers
now I will solve it just for fun..
4x= -18
x= -4.5
ana hikes at a constant speed.She travels 6 miles in 2 hours. Find her speed in miles per hour.Use it to write an equation for the distance ,d, that ana travels in h hours.
Answers
d/t=s
Answer:
6mi=2hours
3mi=1hour
so she can go 3mph
Find the orthocenter of ABC
Answers
Answer:
(7,3)
Step-by-step explanation:
Haley is considering two gym membership plans. The plans are detailed here. Plan one $50 for a monthly pass and a $3 fee for each gym visit plan to $10 for each gym visit what is a system of equations that represents the cost of the plans?
Answers
The two situations can be represented as C(x) = 3x + 50 and C(x) = 10x.
What is the graphical solution of a system of equations?Graphical solutions of a system of equations are way of finding the intersection points of all the equations given.
A system with two or more than two equations has a solution only when they have a common intersection point.
Let the no. of gym visits be 'x' and the total cost be C(x).
Given, Plan one $50 for a monthly pass and a $3 fee for each gym visit.
∴ C(x) = 3x + 50.
Plan two $10 for each gym visit.
∴ C(x) = 10x.
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Three different hoses, each with its own pump, can be used to fill a swimming pool. If hose A is used by itself, the pool takes 6 h to fill. Is hose B is used by itself, the pool takes 3 h to fill. If hose C is used by itself, the pool takes 2 h to fill. If all three hoses are used at the same time, how long does the pool take to fill?
Answers
Find an equivalent mixed number for the decimal number 2.64
A. 2 32/100
B. 2 64/50
C. 2 37/50
D. 2 16/25
Answers
Answer:
d) 2 16/25
Step-by-step explanation:
Now we have to,
→ convert into mixed fraction.
Let's solve the problem,
→ 2.64
→ (264/100)
→ 2 64/100
→ 2 16/25
Hence, option (d) is correct.
What is the slope of the line?
y = 5 + 4x
Question 5 options:
a) 5
b) 9
c) 1
d) 4
Answers
The answer is to your question is B)4. Its y=mx+b and m is your slope and 4 is thw m.
a football team lost 4yards on each of 2 plays,gained 14 yards on the thrid play and lost 5 yards on the fourth play.
Answers
When comparing answers on a group assignment, Jenny and Jeremy found that their answers did not match.
Part 1: Who do you believe has the correct solution for the group assignment—Jenny or Jeremy? In two or more complete sentences, explain, in mathematical terms, the reasoning behind your conjecture.
Part 2: Use long division to convert the fraction provided in each of the student's answers to a decimal number. Include all of your calculations in your final answer.
Part 3: Using complete sentences, compare your conjecture in Part 1 with your results in Part 2. Was your conjecture correct or incorrect?
Answers
The decimal number would be 0.41.
which expression is the same as 2(n+7)
Answers
distribute the 2 to both n and 7
They are being multiplied after distribution, so A is your best answer
hope this helps
In a particular card game, the minimum score a player can achieve in a single game is 20, and the maximum score possible in a single game is 52. If a player plays three games and scores a total of 141 points, what is the least number of points that the player could have scored in one of the games?
Answers
So if both got 52, the total points would be 104, for two games of 52 points. Since we want 141 points, we therefore want 37 more points to reach 141.
So the least amount of points a player could've scored in one of the games was 37.
If a ball rotates through 110 degrees in 8 seconds, how many rotations does it make in 32 seconds
Answers
If:
110....> 8 seconds
x........32 seconds
Cross multiply
8 * x = 32 * 110
8x = 3520
x = 3520/8
x= 440
It makes 440 rotations in 32 seconds
I hope this helps!
There are 64 teams in a basketball tournament each team has 14 players. How many basketball players in all are in the tournament
Answers
What are the length and width of a rectangle if the length exceeds the width by 75 inches and the perimeter is 158 inches
Answers
or width of 77 and length of 2
or width of 78 and length of 1
they all have a perminiter of 158 and all widths exceed 75