The equation of a line in the slope intercept form is expressed as
y = mx + c
where
m = slope
c = y intercept
The formula for calculating slope is expressed as
m = (y2 - y1)/(x2 - x1)
where
y2 and y1 are the y coordinates of the final and initial points on the line
x2 and x1 are the x coordinates of the final and initial points on the line
We would consider the point at the top and the next point. We have
when x1 = - 5, y1 = 9
when x2 = - 4, y2 = 6
By substituting these values into the slope formula,
m = (6 - 9)/(- 4 - - 5) = - 3/(- 4 + 5) = - 3/1
m = - 3
The y intercept is the value of y at the point where the line passes through the y or vertical axis. From the graph, c = - 6
By substituting m = - 3 and c = - 6 into the slope intercept equation, the equation of the line is
y = - 3x - 6