Answer:
c) an = -13+7(n-1)
Step-by-step explanation:
We can use the formula for arithmetic sequences
an =a1+d(n-1)
where a1 is the first term in the sequence
d is the common difference
and n is the term number
a1 is -13
d is found by taking the second term and subtracting the first term
d = -6--13
= -6+13
d=7
We are adding 7 each time
Substituting what we know,
an = -13 + 7(n-1)
The answer is:
c) [tex]a_{n}=-13+7(n-1)[/tex]Need help with dilation with a scale factor of 1/2 centered at (−1, 3)
A scale factor of 1/2 makes the triangle half the size of the original.
The original is 4 units tall, so 1/2 scale makes the new one 2 units tall.
It is 6 units long, so 1/2 would be 3 units long.
Now since the scale factor is centered at (-1,3) fine the midpoint between The top left corner of the triangle and the center point:
Midpoint ( -1-5/2 , 3+7/2)
Midpoint = (-6/2 , 10/2)
Midpoint = -3,5
This is where the top left corner of the scaled triangle would be.
See attached picture:
A baker made 60 muffins for a cafe. By noon, 45% of the muffins were sold. How many muffins were sold by noon?
Answer:
27 muffins.
Step-by-step explanation:
We have been given that a baker made 60 muffins for a cafe. By noon, 45% of the muffins were sold.
To find the number of muffins sold by noon let us find 45% of 60.
[tex]\text{The number of muffins sold by noon}=\frac{45}{100}\times 60[/tex]
[tex]\text{The number of muffins sold by noon}=0.45\times 60[/tex]
[tex]\text{The number of muffins sold by noon}=27[/tex]
Therefore, 27 muffins were sold by noon.
The expression 1/2bh gives the area of a triangle where b is the base of the triangle and h is the height of the triangle. What is the area of a triangle with the base of 7cm and a height of 4 cm?
[tex]A_{\triangle}=\dfrac{1}{2}bh\\\\\text{We have}\ b=7cm,\ h=4cm\\\\\text{Substitute:}\\\\A_{\triangle}=\dfrac{1}{2}(7)(4)=\dfrac{28}{2}=\boxed{14\ cm^2}[/tex]
Consider the triangles shown. If mUTV < mUTS < mSTR, which statement is true?
Answer:
The true statement is UV < US < SR ⇒ 1st statement
Step-by-step explanation:
"I have added screenshot of the complete question as well as the
diagram"
* Lets revise the hinge theorem
- If two sides of one triangle are congruent to two sides of another
triangle, and the measure of the included angle between these two
sides of the first triangle is greater than the measure of the included
angle of the second triangle then the length of the third side of the
first triangle is longer than the length of the third side of the second
triangle
* Lets solve the problem
- The figure has three triangles have a common vertex T
- m∠UTV < m∠UTS < m∠STR
- From the hinge theorem above
∵ The side opposite to ∠UTV is VU
∵ The side opposite to ∠UTS is US
∵ The side opposite to ∠STR is SR
∵ m∠UTV < m∠UTS < m∠STR
∴ UV < US < SR
* The true statement is UV < US < SR
Answer:
VU<US<SR by the hinge theorem
Step-by-step explanation:
m∥n, m∠1 = 50°, m∠2 = 48°, and line s bisects ∠ABC. What is m∠3?
Answer
m<3 = 49°
Step-by-step explanation:
It is given that,
M∥n, m∠1 = 50°, m∠2 = 48°, and line s bisects ∠ABC
m<DEF = m<1 + m<2 = 50° + 48° = 98°
Corresponding angle of <DEF is equal to <ABC = 98°
To find m<3
< 4 = <5 = 98/2 = 49° (Since line s bisects ∠ABC)
Therefore,
m<3 = 49° (< 4 and <3 are vertically opposite angles)
Answer:
m∠3 = 49°
Step-by-step explanation:
We are given that the angles m∠1 = 50° and m∠2 = 48° and the line s bisects ∠ABC.
If m∠1 = 50° and m∠2 = 48°, then ∠DEF = 50 + 48 = 98°
So ∠DEB will be equal to = 180 - 98 = 82°
If ∠DEB = 82°, then the angle from A to B will 180 - 82 = 98°.
We know that the line s bisects ∠ABC, therefore the measure of angle m∠3 will be half of 98 = 49°
Write an equation of a line that has a y intercept of (0,6) and is parallel to 3x+2y=4
In basketball game, elena scores twice as many points as tyler.Tyler scores four points fewer than noah,and noah scores three times as many points as mai if mai scores 5 points how many points did elena score explainyour reasoning
Answer:
Step-by-step explanation:
Start at the end and work backwards to do this one. Mai scored 5 points.
If Noah scores three times what Mai scores, then:
Noah = 3(5) = 15
If Tyler scores 4 points less than Noah, then:
Tyler = 15 - 4 = 11
If Elena scores twice what Tyler scores, then:
Elena = 2(11) = 22
Together, Dulcina and Hannah have 78 refrigerator magnets. Hannah has 2 times as many refrigerator magnets as Dulcina. How many refrigerator magnets are in Hannah's collection? How many refrigerator magnets are in Dulcina's collection?
Final answer:
Dulcina has 26 refrigerator magnets and Hannah has 52, which is 2 times the number of Dulcina's magnets. They have 78 magnets in total.
Explanation:
The question involves a simple algebra problem. Let's say Dulcina has x refrigerator magnets. According to the problem statement, Hannah has 2 times as many refrigerator magnets as Dulcina, so she has 2x magnets. Together, they have 78 magnets, which means x + 2x = 78. To find out how many refrigerator magnets each has, we need to solve for x.
Combine like terms:
3x = 78
Divide both sides by 3 to solve for x:
x = 26
Now, to find the number of refrigerator magnets Hannah has, we multiply x by 2:
2x = 2 × 26 = 52
What is the trigonometric ratio for sin S ?
Express your answer, as a simplified fraction.
[tex]QR=\sqrt{68^2-60^2}\\QR=\sqrt{4624-3600}\\QR=\sqrt{1024}\\QR=32\\\\sinS=\frac{32}{68}\\sinS=\frac{8}{17}[/tex]
For this case, we have that by definition:
Be a rectangular triangle and an "x" angle.
[tex]Sine (x) = \frac {CO} {H}[/tex]
CO is the leg opposite the angle and H the hypotenuse
We want to find the Sine (S) according to the figure shown:
[tex]Sine {S} = \frac {QR} {68}[/tex]
We do not have the opposite leg, we must apply the Pythagorean theorem, which states:
[tex]H = \sqrt {(CO) ^ 2 + (CA) ^ 2}[/tex]
Where:
H: Hypotenuse
CO: Opposite leg
CA: Adjacent leg
In this case, we must find CO:
[tex]CO = \sqrt {H ^ 2- (CA) ^ 2}[/tex]
Where:
[tex]H = 68\\CA = 60[/tex]
Substituting:
[tex]CO = \sqrt {68 ^ 2-60 ^ 2}\\CO = \sqrt {4624-3600}\\CO = \sqrt {1024}\\CO = 32[/tex]
So, we have:
[tex]Sine (S) = \frac {32} {68}[/tex]
Answer:
[tex]Sine (S) = \frac {32} {68}[/tex]
[tex]Sine (S) = \frac {8} {17}[/tex]
please help fast ill give brainliest
Answer:
5y + 4 and 7y + 4 - 2y
Step-by-step explanation:
Look at the second choice:-
5y + 4 and 7y + 4 - 2y
Simplifying the second expression:-
7y + 4 - 2y
= 5y + 4
So both expressions are equivalent . Therefore if you plug in 2 or 5 the results will be the same.
Answer:
Second option:
5y+4 and 7y+4-2y
Step-by-step explanation:
1. y=2→2y-1=2(2)-1=4-1→2y-1=3
y=2→3y-5+y→3(2)-5+2=6-5+2→3y-5+y=3
y=5→2y-1=2(5)-1=10-1→2y-1=9
y=5→3y-5+y→3(5)-5+5=15-5+5→3y-5+y=15
2y-1 is not equivalent to 3y-5+y when y=2 and y=5
2. y=2→5y+4=5(2)+4=10+4→5y+4=14
y=2→7y+4-2y→7(2)+4-2(2)=14+4-4→7y+4-2y=14
y=5→5y+4=5(5)+4=25+4→5y+4=29
y=5→7y+4-2y→7(5)+4-2(5)=35+4-10→7y+4-2y=29
5y+4 is equivalent to 7y+4-2y when y=2 and y=5
3. y=2→y+7=2+7→y+7=9
y=2→y+2+y→2+2+2→y+2+y=6
y+7 is not equivalent to y+2+y when y=2 and y=5
4. y=2→3y-4=3(2)-4=6-4→3y-4=2
y=2→3y-2+y→3(2)-2+2=6-2+2→3y-2+y=6
3y-4 is not equivalent to 3y-2+y when y=2 and y=5
Combine like terms . What is a simpler form of the expression? 2(x/2 -5)-3/2(x+7/4). Please Explain.
The value of x is -101/4 or the simplified form of the expression can be given as -1/2x = 101/8
This question relates to equation in mathematics and all we need to do is solve for x. But this requires some step by step process which are
open the bracketcollect like termsdivide through by the coefficient of xThe given equation is
[tex]2(\frac{x}{2} - 5) - \frac{3}{2} (x+\frac{7}{4} )\\[/tex]
Open Bracket[tex]2(\frac{x}{2} - 5) - \frac{3}{2} (x+\frac{7}{4} )\\\\(\frac{2}{2}x-10)-(\frac{3}{2}x-\frac{21}{8}) \\x- 10 -\frac{3}{2}x-\frac{21}{8}\\[/tex]
Collect like terms[tex]x-\frac{3}{2}x-10-\frac{21}{8}=0\\-\frac{1}{2}x =10+\frac{21}{8}\\-\frac{1}{2}x=101/8\\[/tex]
Divide ThroughWe have to divide through by coefficient of x
[tex]-\frac{1}{2}x =\frac{101}{8}\\(-1/2x)/(-1/2)=(101/8)/(-1/2)\\x=\frac{-101}{4} \\[/tex]
from the above calculation, the value of x is -101/4. The simplified form of the expression is -1/2x = 101/8
Learn more about equation here;
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3. Use the SUBSTITUTION method to solve this system of equations:
Answer: (2, 9)
Step-by-step explanation:
[tex]\lbrace^{y=5x-1 }_{2y=3x+12}}[/tex]
Since "y" = "5x - 1", we can replace "y" in the second equation with "5x - 1"
2y = 3x + 12
⇒ 2(5x - 1) = 3x + 12 substituted "y" with "5x - 1"
⇒ 10x - 2 = 3x + 12 distributed 5x - 1 by 2 on left side
⇒ 7x - 2 = 12 subtracted 3x from both sides
⇒ 7x = 14 added 2 to both sides
⇒ x = 2 divided both sides by 2
Next, let's solve for y by substituting "x" with "2":
y = 5x - 1
= 5(2) - 1
= 10 - 1
= 9
Justin and Jason are building a fort. They need 250 pieces of wood. Justin can hammer 10 1/4 pieces of wood an hour. Jason can hammer 9 1/2 in one hour. How many hours will it take them to finish the fort?
Answer: 12 hours
Step-by-step explanation:
1.) add 10 1/4 and 9 1/3. You’ll get 19.75
2.) divide 250 by 19.75. You’ll get something close to 12.6582278481 if you use appendix zeros.
3.) round 12.6582278481 to the nearest whole number. It will be 12. Hope this helps :)
5. What is the median of the data displayed in the box-and-whisker plot?
6. What is the highest value of the data displayed in the box-and-whisker plot?
7. What us the upper quartile of the data displayed in the box -and-whisker plot?
Answer:
5. 20
6. 30
7. 22
Step-by-step explanation:
5. The median is indicated by the line (and dot) in the middle of the box.
6. The maximum value is indicated by the extreme right end of the whisker.
7, The upper quartile is indicated by the right end of the box.
Answer:
5. 20
6. 30
7. 22
Step-by-step explanation:
5. The median is indicated by the line (and dot) in the middle of the box.
6. The maximum value is indicated by the extreme right end of the whisker.
7, The upper quartile is indicated by the right end of the box.
Banks also provide special services such as a. help with taxes. c. mortgage loans. b. financial planning. d. all of the above.
Answer:the answer is D. All of the above
Step-by-step explanation:
Answer:
D) ALL OF THE ABOVE
Explanation:
In today's world, banks offer various variety of services at door-steps to attract customers However, some basic today's services offered by the banks to its customers are discussed below:
Home bankingOnline bankingPriority banking1. Home banking:
Home banking is the procedure of finishing financial affairs from an individual's own home as opposed to using a branch of a bank. It compromises actions such as transferring money, applying for loans, paying bills, making financial inquires and directing deposits.
2. Online banking:
Online banking is one of the famous service offered by banks nowadays that allows customers to access their account data by using the internet. Online banking is also known as “Internet banking”.
3. Priority banking:
Priority banking may include various services, but some of the famous services include online bill pay, financial consultation, free checking of account amount and information.
If sinX= 0.9, what is the value of cos X?
Round the value to the nearest thousandth.
Answer: sqrt(19)/10
Step-by-step explanation:
sinx=0.9
x=arcsin(0.9)
Insert x for cos(x):
cos(arcsin(0.9)=
Use identify [tex]cos(arcsin(x))=\sqrt{1-x^{2} }[/tex], so
[tex]\sqrt{1-(\frac{9}{10})^{2}} =\sqrt{\frac{19}{100} } =\frac{\sqrt{19}}{10}[/tex]
Sorry if this is confusing.
Final answer:
To find cos X given sin X = 0.9, use the Pythagorean identity, solve for cos2 X, take the square root, and round to the nearest thousandth to get cos X ≈ 0.436.
Explanation:
To calculate the value of cos X when sin X= 0.9, we can use the Pythagorean identity which states that sin2X + cos2X = 1. First, square the sine value: (sin X)2 = 0.92 = 0.81. Then, we subtract this value from 1 to find (cos X)2: 1 - 0.81 = 0.19. Finally, we take the square root of 0.19 to find the value of cos X. Since sin X is positive and assuming X is an angle in the first quadrant, cos X will also be positive. So, cos X = √0.19 ≈ 0.436.
Therefore, the value of cos X, rounded to the nearest thousandth, is 0.436.
The area of a rectangle is 180 squared in2. The ratio of the length to the width is 5 : 4Find the length and the width. The length of the rectangle is nothing in.
180 in² - the area
width × lenght - the area
length : width = 5 : 4 therefore length = 5x and width = 4x
(x - some unit of length)
The equation:
(5x)(4x) = 180
20x² = 180 divide both sides by 20
x² = 9 → x = √9 → x = 3 in.
The length = 5x, therefore your answer is:
5x = 5(3 in) = 15inA line is represented by the equation x + 2y = 4. What is the slope and y-intercept?
The slope of the equation x + 2y = 4, is -1/2 and y-intercept of the equation is 2.
What is the slope intercept form of an equation ?When any equation is represented in the y = m x +c form, it is called the slope intercept form of the equation.
Here m is slope and c is constant.
The given equation of line,
x + 2y = 4,
To find the slope, represent the equation in slop intercept form,
Simplify the equation,
x + 2y = 4
2y = -x + 4
y = -(1/2)x + 2
The slope of the equation is -1/2.
To find y-intercept, substitute x = 0,
y = -(1/2). 0 + 2
y = 2
The y-intercept of the equation is 2.
To know more about Slope intercept form :
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A rectangular garden has a length of 2m+17 feet and a width of 3m feet. Which expression represents the area
Answer:
area = 6m + 51 feet²
Step-by-step explanation:
area = length × width = 3(2m + 17) = 6m + 51
Judy worked 8 hours and Ben worked 10 hours. Their combined pay was $80. When Judy worked 9 hours and Ben worked 5 hours, their combined pay was $65. Find the hourly rate of pay for each person
Answer:
Judy = $5/hr
Ben = $4/hr
Step-by-step explanation:
Judy's hours at work - x
Ben's hours at work - y
8x + 10y = 80
9x + 5y = 65
Given these two equations above, we get:
10y = 80 - 8x, which means y = 8 - 0.8x.
Substitute y in the second equation with 8 - 0.8x, so we have:
9x + 5 (8 - 0.8x) = 65
9x + 40 - 4x = 65
5x = 25
x = 5
Come back to the first equation, substitute x:
8*5 + 10y = 80
10y = 80 - 40
y = 4
If the sum of x and 14 is 18, then the product of x and 4 is?
Answer:
16
Step-by-step explanation:
sum of x and 14 is 18
x+14 = 18
Subtract 14 from each side
x+14-14 = 18-14
x = 4
product of x and 4
x*4
4*4
16
Answer:
16
18 minus 14 is 4. 4 times 4 is 16.
Which statement is the Law of Detachment? A. If p q is a true statement and q is true, then p is true. B. If p q is a true statement and q is true, then q p is true. C. If p q and q r are true, the p r is a true statement. D. If p q is a true statement and p is true, then q is true.
Answer:
Its D
Step-by-step explanation:
If p then q. If p is true then q is true.
Answer:
it's number d
Step-by-step explanation:
Marcus stated that any time an integer is raised to an integer exponent, the result is a rational number.
Is Marcus correct? Why or why not?
Select the option that is completely correct.
Marcus is incorrect. If any integer is raised to a negative integer exponent, the base is multiplied repeatedly. The product of two integers may not be a rational number.
Marcus is correct. If any integer is raised to any integer exponent, the base is multiplied or divided repeatedly. The product or quotient of integers is always a rational number.
Marcus is incorrect. If any integer is raised to a negative integer exponent, the base is divided repeatedly. The quotient of two integers may not be a rational number.
Marcus is correct. If any integer is raised to any integer exponent, the base is multiplied times the exponent. The product of two integers is always a rational number.
Final answer:
Marcus is incorrect, not because the result may not be rational, but because of his reasoning. An integer raised to a negative integer exponent leads to the base being inverted and raised to the positive exponent, but the result is still a rational number.
Explanation:
Marcus is incorrect in stating that any time an integer is raised to an integer exponent, the result is a rational number. To understand why, we should look at the case when an integer is raised to a negative integer exponent. For example, 3-2 is equal to 1 / (32) which simplifies to 1 / 9. A negative exponent inverts the base number and raises it to the positive of that exponent, which means the result is still a rational number, as it's a quotient of two integers. Therefore, the correct statement is that the result of an integer raised to any integer exponent is indeed a rational number, as the quotient of two integers (for negative exponents) is also a rational number.
Susan's penny bank is 1/10 full. After she adds 240 pennies, it is 2/5 full. How many pennies can Susan's bank hold?
Answer:
240 pennies occupy (2/5 minus 1/10) the penny bank volume.
2/5 - 1/10 = 3/10 = .3
240 pennies .3 * the volume
Volume = 240 / .3 = 800 pennies
Step-by-step explanation:
If f(x) varies directly with x and f(x) = 4 when x = 12, then what is the value of f(x) when x = 60?
20
180
5
300
Help me with these math questions..... WITH SCREENIES
[tex]adj(x) = \frac{\sqrt{7}}{3}[/tex]
[tex]opp(y) = \frac{\sqrt{2}}{3}[/tex]
adj² + opp² = hyp²
[tex](\frac{\sqrt{7}}{3})^{2} +(\frac{\sqrt{2}}{3})^{2} = hyp^{2}[/tex]
[tex]\frac{7}{9} +\frac{2}{9} = hyp^{2}[/tex]
1 = hyp²
1 = hyp
sin = [tex]\frac{opp}{hyp} =\frac{\sqrt{2}}{3}[/tex]
cos = [tex]\frac{adj}{hyp} =\frac{\sqrt{7}}{3}[/tex]
tan = [tex]\frac{opp}{adj} =\frac{\sqrt{2}}{sqrt\{7}=\frac{\sqrt{14}}{7}}[/tex]
csc = [tex]\frac{hyp}{opp} =\frac{3}{sqrt\{2}=\frac{3\sqrt{2}}{2}}[/tex]
sec = [tex]\frac{hyp}{adj} =\frac{3}{sqrt\{7}=\frac{3\sqrt{7}}{7}}[/tex]
cot = [tex]\frac{adj}{opp} =\frac{\sqrt{7}}{sqrt\{2}=\frac{\sqrt{14}}{2}}[/tex]
****************************************************************
Answer: 8052
Step-by-step explanation:
[tex]A = Pe^{kt}[/tex]
[tex]5500 = 5000e^{k(3)}[/tex]
[tex]\frac{5500}{5000} = e^{3k}[/tex]
[tex]1.1 = e^{3k}[/tex]
[tex]ln1.1 = lne^{3k}[/tex]
ln1.1 = 3k
[tex]\frac{ln1.1}{3}=k[/tex]
0.03177 = k
[tex]A = Pe^{0.03177t}[/tex]
[tex]A = 5500e^{0.03177(12)}[/tex]
[tex]A = 5500e^{0.3812}[/tex]
[tex]A = 5500(1.4641)}[/tex]
A = 8052.55
****************************************************************
Answer: (2, 9)
Step-by-step explanation:
3x - 8y = -66 → 2(3x - 8y = -66) → 6x - 16y = -132
2x - 7y = -59 → -3(2x - 7y = -59) → -6x + 21y = 177
5y = 45
y = 9
2x - 7y = -59
2x - 7(9) = -59
2x - 63 = -59
2x = 4
x = 2
PLEASE HELP ASAP!!! CORRECT ANSWERS ONLY PLEASE!!!
The graph shows the solution to which system of equations?
Answer:
C
Step-by-step explanation:
The lines drawn have the following features:
Y-intercepts of 1 and -3Slopes of -2 and 2.Since the equation of a line has the form y=mx+b where b is y-intercept and m is the slope, we can write
y=-2x+1
y=2x-3
This is the system of equations and is answer choice C.
Answer: C
Step-by-step explanation:
Slope-Intercept form of an equation is y = mx + b
m is slope (rise over run)b is y-intercept (where it crosses the y-axis)Red line:
It crosses the y-axis at -3 so b = -3
Now count the rise over run from the b (0, -3) to another point (I chose (1, -1) because it was the next point on a lattice line). The rise is 2 and the run is 1. So. rise over run is 2/1 ⇒ m = 2
Equation: y = 2x - 3
Yellow line:
Follow the same steps as the Red line to get b = 1 and m = -2
Equation: y = -2x + 1
Verify the identity. 4 csc 2x = 2 csc2x tan x
Step-by-step explanation:
[tex]4csc(2x) = 2csc^2(x) tan(x)[/tex]
We start with Left hand side
We know that csc(x) = 1/ sin(x)
So csc(2x) is replaced by 1/sin(2x)
[tex]4 \frac{1}{sin(2x)}[/tex]
Also we use identity
sin(2x) = 2 sin(x) cos(x)
[tex]4 \frac{1}{2sin(x)cos(x)}[/tex]
4 divide by 2 is 2
Now we multiply top and bottom by sin(x) because we need tan(x) in our answer
[tex]2\frac{1*sin(x)}{sin(x)cos(x)*sin(x)}[/tex]
[tex]2\frac{sin(x)}{sin^2(x)cos(x)}[/tex]
[tex]2\frac{1}{sin^2(x)} \frac{sin(x)}{cos(x)}[/tex]
We know that sinx/ cosx = tan(x)
Also 1/ sin(x)= csc(x)
so it becomes 2csc^2(x) tan(x) , Right hand side
Hence verified
What is the standard form of an ellipse with foci at (0, ±2), and vertices at (0, ±4)?
See the attached picture.
please answer this!!
Answer:
Use point slope form, by finding the slope between two of the points given on the line you can then input it with one of the points into the formula. Then simplify to convert to slope-intercept form. You can then graph it easily. After which, you can convert to standard form by getting the variables to one side. Be sure in standard form to clear negatives x may have or any fractions x or y may have through multiplication.
Step-by-step explanation:
To write an equation for linear equations, we use one of three forms: standard, slope intercept, and point slope. Slope intercept and point slope are the most common. After we choose our form, we need to find the information required for that form. Point slope is easiest since it requires the slope/rate of change and any point on the line.
Point slope:[tex]y-y_1=m(x-x_1)[/tex]
We must find the slope using the slope formula.
Slope:[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]
We substitute [tex]x_1=-3\\y_1=1[/tex] and [tex]x_2=3\\y_2=5[/tex]
[tex]m=\frac{5-1}{3-(-3)}[/tex]
[tex]m=\frac{4}{3+3}=\frac{4}{6} =\frac{2}{3}[/tex]
We will substitute [tex]m=\frac{2}{3}[/tex] and [tex]x_1=-3\\y_1=1[/tex].
[tex]y-1=\frac{2}{3} (x-(-3))[/tex]
We can simplify to get slope intercept form:
[tex]y-1=\frac{2}{3} (x+3))[/tex]
[tex]y-1=\frac{2}{3}x+\frac{2}{3}(3)[/tex]
[tex]y-1=\frac{2}{3}x+2[/tex]
[tex]y-1+1=\frac{2}{3}x+2+1[/tex]
[tex]y=\frac{2}{3}x+3[/tex]
This is the slope intercept form. We can graph it by finding 3 on the y-axis. Plot a point there. Then move up two units and to the right three units. Plot a point. Connect the points.
To convert to Standard Form, we will rearrange the equation with x and y on the same side.
[tex]y=\frac{2}{3}x+3[/tex]
[tex]-\frac{2}{3}x+y=\frac{2}{3}x-\frac{2}{3}x+3[/tex]
[tex]-\frac{2}{3}x+y=3[/tex]
[tex]-3(-\frac{2}{3}x+y=3)[/tex]
[tex] 2x-3y=-9[/tex]
This is the standard form.