A line passes through the points (–12,3) and (16,–18). Write its equation in slope-intercept form.

Step 1: Find the slope of the line

The slope of a line passing through two points (x1, y1) and (x2, y2) is given by the formula:

m = (y2 - y1) / (x2 - x1)

Substituting the given points (-12, 3) and (16, -18) into the formula, we get:

m = (-18 - 3) / (16 - (-12)) = -21 / 28 = -3/4

So, the slope of the line is -3/4.

Step 2: Write the equation of the line in point-slope form

The point-slope form of a line is given by the formula:

y - y1 = m(x - x1)

Substituting the slope we found and one of the given points into the formula, we get:

y - 3 = -3/4(x - (-12))

Step 3: Simplify the equation to slope-intercept form

The slope-intercept form of a line is given by the formula:

y = mx + b

To get this form, we need to distribute the slope on the right side of the equation and then add 3 to both sides:

y - 3 = -3/4x - 9 y = -3/4x - 9 + 3 y = -3/4x - 6

So, the equation of the line in slope-intercept form is y = -3/4x - 6.