A line passes through the points (2,–2) and (3,–9). Write its equation in slope-intercept form.

Step 1: Find the slope of the line

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

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

Substituting the given points (2, -2) and (3, -9) into the formula, we get:

m = (-9 - (-2)) / (3 - 2) = -7

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

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

y = mx + b

where m is the slope and b is the y-intercept. We already know that m = -7. To find b, we can substitute one of the given points and the slope into the equation. Let's use the point (2, -2):

-2 = -7*2 + b -2 = -14 + b b = -2 + 14 = 12

So, the equation of the line in slope-intercept form is:

y = -7x + 12