Answer:
Please check the explanation.
Step-by-step explanation:
Given the equation
![-x + 2y = 4](https://tex.z-dn.net/?f=-x%20%2B%202y%20%3D%204)
a) writing the equation in the slope-intercept form
We know that the slope-intercept form of the equation of the line is
![y=mx+b](https://tex.z-dn.net/?f=y%3Dmx%2Bb)
where m is the slope of the line
so writing the equation in the slope-intercept form
![-x + 2y = 4](https://tex.z-dn.net/?f=-x%20%2B%202y%20%3D%204)
![2y=4+x](https://tex.z-dn.net/?f=2y%3D4%2Bx)
![y=\frac{1}{2}x+2](https://tex.z-dn.net/?f=y%3D%5Cfrac%7B1%7D%7B2%7Dx%2B2)
b) Identify the slope of the line represented in part a
As the equation in slope-intercept form is
![y=\frac{1}{2}x+2](https://tex.z-dn.net/?f=y%3D%5Cfrac%7B1%7D%7B2%7Dx%2B2)
Here,
m = slope = 1/2 ∵ ![y=mx+b](https://tex.z-dn.net/?f=y%3Dmx%2Bb)
c) What is the slope of the line perpendicular to the line in steps a and b
As we know that the slope of the perpendicular line is basically the negative reciprocal of the slope of the line, so
As the slope = 1/2
So the slope of the perpendicular line will be: -2
d. Write the equation of the perpendicular line in slope-intercept form.
Therefore, the point-slope form of the equation of the perpendicular line that goes through (-2,1) is:
![y-y_1=m\left(x-x_1\right)](https://tex.z-dn.net/?f=y-y_1%3Dm%5Cleft%28x-x_1%5Cright%29)
substituting the values m = -2 and the point (-2,1)
![\:y-1=-2\left(x-\left(-2\right)\right)](https://tex.z-dn.net/?f=%5C%3Ay-1%3D-2%5Cleft%28x-%5Cleft%28-2%5Cright%29%5Cright%29)
![y-1=-2\left(x+2\right)](https://tex.z-dn.net/?f=y-1%3D-2%5Cleft%28x%2B2%5Cright%29)
Add 1 to both sides
![y-1+1=-2\left(x+2\right)+1](https://tex.z-dn.net/?f=y-1%2B1%3D-2%5Cleft%28x%2B2%5Cright%29%2B1)
![y=-2x-3](https://tex.z-dn.net/?f=y%3D-2x-3)