A line passes through the points (–2,6) and (1,–9). Write its equation in slope-intercept form.

Step 1: Find the slope of the line. The slope (m) of a line passing through two points (x1, y1) and (x2, y2) is given by the formula:

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

Substitute the given points into the formula:

m = (-9 - 6) / (1 - (-2)) = -15 / 3 = -5

Step 2: Write the equation in slope-intercept form (y = mx + b), where m is the slope and b is the y-intercept.

We already know that m = -5. To find b, we can substitute one of the given points and the slope into the equation and solve for b. Let's use the point (–2,6):

6 = -5*(-2) + b 6 = 10 + b b = 6 - 10 = -4

Step 3: Substitute m and b into the slope-intercept equation:

y = -5x - 4

So, the equation of the line in slope-intercept form that passes through the points (–2,6) and (1,–9) is y = -5x - 4.