Answer:
![y-7=3(x-9)](https://tex.z-dn.net/?f=y-7%3D3%28x-9%29)
Step-by-step explanation:
The form of equation of line given in the problem is the point-slope form of a line. That is given by:
![y-y_1=m(x-x_1)](https://tex.z-dn.net/?f=y-y_1%3Dm%28x-x_1%29)
We need
and m (denoted by boxes)
is the y coordinate of the first set of points.
The first coordinate pair is (9,7), so
would be 7
![y_1=7](https://tex.z-dn.net/?f=y_1%3D7)
Now, the slope (m).
It has formula
![m=\frac{y_2-y_1}{x_2-x_1}](https://tex.z-dn.net/?f=m%3D%5Cfrac%7By_2-y_1%7D%7Bx_2-x_1%7D)
So, x_1 = 9
y_1 = 7
x_2 = 4
y_2 = -8
Substituting, we get the slope to be:
![m=\frac{y_2-y_1}{x_2-x_1}\\m=\frac{-8-7}{4-9}\\m=\frac{-15}{-5}\\m=3](https://tex.z-dn.net/?f=m%3D%5Cfrac%7By_2-y_1%7D%7Bx_2-x_1%7D%5C%5Cm%3D%5Cfrac%7B-8-7%7D%7B4-9%7D%5C%5Cm%3D%5Cfrac%7B-15%7D%7B-5%7D%5C%5Cm%3D3)
Hence, the equation of the line in point-slope is:
![y-7=3(x-9)](https://tex.z-dn.net/?f=y-7%3D3%28x-9%29)