To write the equation of a line in slope-intercept form (y = mx + b), we need to find the slope of the line (m) and the y-intercept (the point where the line crosses the y-axis, which is represented by b).
We can use the point-slope formula to find the equation of the line that passes through the points (-2,-2) and (5,12):
y - y1 = m(x - x1)
Where (x1, y1) is a point on the line, and m is the slope of the line.
Plugging in the values for the given points and solving for m, we get:
m = (12 - (-2)) / (5 - (-2))
= 14 / 7
= 2
Now that we have the slope, we can use either of the given points to find the y-intercept (b). Let's use the point (-2,-2):
y = mx + b
-2 = 2(-2) + b
-2 = -4 + b
b = -2 + 4
b = 2
Therefore, the equation of the line in slope-intercept form is:
y = 2x + 2
This is the equation of the line that passes through the points (-2,-2) and (5,12).