Final answer:
The slope-intercept form of the linear equation is y = 12x + 32.
Step-by-step explanation:
The slope-intercept form of a linear equation is given by y = mx + b, where m is the slope and b is the y-intercept.
In this case, the slope (m) is given as 12.
We are also given a point (-2, 8) that lies on the line.
Using the point-slope form of a linear equation, we can substitute the values of the slope (m), x-coordinate (-2), and y-coordinate (8) into the equation:
y - y1 = m(x - x1)
8 - 8 = 12(-2 - x)
0 = 12(-2 - x)
0 = -24 - 12x
12x = -24
x = -2
Substituting the value of x into the equation, we can solve for y:
y = mx + b
y = 12(-2) + b
y = -24 + b
Since the point (-2, 8) lies on the line, we can substitute the values of x and y into the equation to solve for b:
8 = -24 + b
b = 32
Therefore, the slope-intercept form of the linear equation is y = 12x + 32.