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Q7: ![y = 2x+3](https://tex.z-dn.net/?f=y%20%3D%202x%2B3)
Q8: ![y=-2x+5](https://tex.z-dn.net/?f=y%3D-2x%2B5)
Q9: ![m = -\frac{A}{B}](https://tex.z-dn.net/?f=m%20%3D%20-%5Cfrac%7BA%7D%7BB%7D)
Step-by-step explanation:
Q7: Given equation of line is:
![2x-y=1](https://tex.z-dn.net/?f=2x-y%3D1)
Converting into slope-intercept form
![2x-y-1 = 1-1\\2x-y-1+y = 0+y\\y = 2x-1](https://tex.z-dn.net/?f=2x-y-1%20%3D%201-1%5C%5C2x-y-1%2By%20%3D%200%2By%5C%5Cy%20%3D%202x-1)
Comparing with the standard slope-intercept form
![y = mx+b](https://tex.z-dn.net/?f=y%20%3D%20mx%2Bb)
We get
m = 2
As the new line has same slope as given line
![m_1 = 2](https://tex.z-dn.net/?f=m_1%20%3D%202)
Given
b = 3
The equation is given by:
![y = m_1x+b](https://tex.z-dn.net/?f=y%20%3D%20m_1x%2Bb)
Putting the values of slope and y-intercept
![y = 2x+3](https://tex.z-dn.net/?f=y%20%3D%202x%2B3)
Q8: Given equation of line is:
![6x+3y = 12](https://tex.z-dn.net/?f=6x%2B3y%20%3D%2012)
converting in slope-intercept form
![3y = -6x+12](https://tex.z-dn.net/?f=3y%20%3D%20-6x%2B12)
Dividing both sides by 3
![y = -2x+4](https://tex.z-dn.net/?f=y%20%3D%20-2x%2B4)
The slope of line is: -2
The new line has same slope so,
m_1 = -2
Slope-intercept form of line is:
![y = m_1x+b](https://tex.z-dn.net/?f=y%20%3D%20m_1x%2Bb)
Putting the value of slope
![y = -2x+b](https://tex.z-dn.net/?f=y%20%3D%20-2x%2Bb)
Putting the point (2,1) in the equation
![1 = -2(2) +b\\1 = -4 +b\\b = 4+1\\b = 5](https://tex.z-dn.net/?f=1%20%3D%20-2%282%29%20%2Bb%5C%5C1%20%3D%20-4%20%2Bb%5C%5Cb%20%3D%204%2B1%5C%5Cb%20%3D%205)
So the equation is:
![y=-2x+5](https://tex.z-dn.net/?f=y%3D-2x%2B5)
Q9: Given equation is:
![Ax+By = C](https://tex.z-dn.net/?f=Ax%2BBy%20%3D%20C)
subtracting Ax from both sides
![Ax+By-Ax = C-Ax\\By = -Ax+C](https://tex.z-dn.net/?f=Ax%2BBy-Ax%20%3D%20C-Ax%5C%5CBy%20%3D%20-Ax%2BC)
Dividing both sides by B
![\frac{By}{B} = \frac{-Ax+C}{B}\\y = -\frac{A}{B}x + \frac{C}{B}](https://tex.z-dn.net/?f=%5Cfrac%7BBy%7D%7BB%7D%20%3D%20%5Cfrac%7B-Ax%2BC%7D%7BB%7D%5C%5Cy%20%3D%20-%5Cfrac%7BA%7D%7BB%7Dx%20%2B%20%5Cfrac%7BC%7D%7BB%7D)
As the equation is in slope-intercept form, the co-efficient of x is the slope of line
So the slope is:
![m = -\frac{A}{B}](https://tex.z-dn.net/?f=m%20%3D%20-%5Cfrac%7BA%7D%7BB%7D)
Hence,
Q7: ![y = 2x+3](https://tex.z-dn.net/?f=y%20%3D%202x%2B3)
Q8: ![y=-2x+5](https://tex.z-dn.net/?f=y%3D-2x%2B5)
Q9: ![m = -\frac{A}{B}](https://tex.z-dn.net/?f=m%20%3D%20-%5Cfrac%7BA%7D%7BB%7D)
Keywords: Equation of line, slope
Learn more about equation of line at:
#LearnwithBrainly
Answer:
x+y =13
10x + 9y =122
Step-by-step explanation:
Hi, to answer this question we have to write a system of equations:
The sum of the hours he worked washing cars (x) and the hours he worked walking dogs(y) will be equal to the total hours worked (13)
For the second equation the product of the number of hours he worked washing cars(x) and the price per hour ($10) plus the product of the number of hours he worked walking dogs (y) and the price per hour ($9) will be equal to the total amount earned (122)-
So, the system of equations is:
Where:
x: number of hours Jose worked washing cars
y: number of hours Jose worked walking dogs
The answer is x = {-1, 9}
Hope this helped Mark me as brainliest pls