Answer:
[tex]y-7=3(x-9)[/tex]
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:
[tex]y-y_1=m(x-x_1)[/tex]
We need [tex]y_1[/tex] and m (denoted by boxes)
[tex]y_1[/tex] is the y coordinate of the first set of points.
The first coordinate pair is (9,7), so [tex]y_1[/tex] would be 7
[tex]y_1=7[/tex]
Now, the slope (m).
It has formula
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]
So, x_1 = 9
y_1 = 7
x_2 = 4
y_2 = -8
Substituting, we get the slope to be:
[tex]m=\frac{y_2-y_1}{x_2-x_1}\\m=\frac{-8-7}{4-9}\\m=\frac{-15}{-5}\\m=3[/tex]
Hence, the equation of the line in point-slope is:
[tex]y-7=3(x-9)[/tex]
