The equation of a line in the slope intercept form is expressed as
y = mx + c
where
m represents slope
c represents y intercept
The formula for calculating slope is expressed as
m = (y2 - y1)/(x2 - x1)
From the information given,
x1 = 9, y1 = - 1
x2 = - 5, y2 = 4
m = (4 - - 1)/(- 5 - 9) = (4 + 1)/- 14
m = - 5/14
We would find the y intercept by substituting m = - 5/14, x = 9 and y = - 1 into the slope intercept equation. It becomes
- 1 = - 5/14 * 9 + c
- 1 = - 45/14 + c
c = - 1 + 45/14 c = 31/14
By substituting m = - 5/14 and c = 31/14 into the slope intercept equation, the equation of the line is
y = - 5x/14 + 31/14