Final answer:
The equation of the line in slope-intercept form is y = (-5/2)x - 2, using the given slope of -5/2 and solving for the y-intercept with the point (-4, 8).
Step-by-step explanation:
To write the equation of a line in slope-intercept form, which is y = mx + b where 'm' represents the slope and 'b' represents the y-intercept, we need to know both the slope and the y-intercept of the line. Since we already have the slope (-5/2) and a point on the line (-4, 8), we can use these to find the y-intercept.
First, we insert the known slope and point into the equation y = mx + b, substituting m with -5/2, x with -4, and y with 8, and solve for b:
8 = (-5/2)(-4) + b
8 = 10 + b
8 - 10 = b
-2 = b
Now that we have the y-intercept, we can write the final equation of the line:
y = (-5/2)x - 2