Answer:
The equation of the line that passes through the points (7,-8) and (2, -8) is ![\mathbf{y=-8}](https://tex.z-dn.net/?f=%5Cmathbf%7By%3D-8%7D)
Step-by-step explanation:
We need to write the equation of the line that passes through the points (7,-8) and (2, -8).
We need to write answer in fully reduced point-slope form, unless it is a vertical or horizontal line.
The general equation of point-slope form is: ![y-y_1=m(x-x_1)](https://tex.z-dn.net/?f=y-y_1%3Dm%28x-x_1%29)
where m is slope of the line.
To find the slope, we can use formula: ![Slope=\frac{y_2-y_1}{x_2-x_1}](https://tex.z-dn.net/?f=Slope%3D%5Cfrac%7By_2-y_1%7D%7Bx_2-x_1%7D)
We have ![x_1=7,y_1=-8,x_2=2, y_2=-8](https://tex.z-dn.net/?f=x_1%3D7%2Cy_1%3D-8%2Cx_2%3D2%2C%20y_2%3D-8)
Putting values and finding slope:
![Slope=\frac{y_2-y_1}{x_2-x_1}\\Slope=\frac{-8-(-8)}{2-7}\\Slope=\frac{-8+8}{-5}\\Slope=\frac{0}{-5}\\Slope=0](https://tex.z-dn.net/?f=Slope%3D%5Cfrac%7By_2-y_1%7D%7Bx_2-x_1%7D%5C%5CSlope%3D%5Cfrac%7B-8-%28-8%29%7D%7B2-7%7D%5C%5CSlope%3D%5Cfrac%7B-8%2B8%7D%7B-5%7D%5C%5CSlope%3D%5Cfrac%7B0%7D%7B-5%7D%5C%5CSlope%3D0)
So, we find the slope : m = 0
Now, using the point (7,-8) and slope m =0, the required equation is:
![y-y_1=m(x-x_1)\\y-(-8)=0(x-7)\\y+8=0\\y=-8](https://tex.z-dn.net/?f=y-y_1%3Dm%28x-x_1%29%5C%5Cy-%28-8%29%3D0%28x-7%29%5C%5Cy%2B8%3D0%5C%5Cy%3D-8)
So, the equation of the line that passes through the points (7,-8) and (2, -8) is ![\mathbf{y=-8}](https://tex.z-dn.net/?f=%5Cmathbf%7By%3D-8%7D)