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
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