A line passes through the points (–2,–10) and (3,5). 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 = (5 - (-10)) / (3 - (-2)) = 15 / 5 = 3

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 = 3. 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 (3,5):

5 = 3*3 + b 5 = 9 + b b = 5 - 9 = -4

Step 3: Substitute m = 3 and b = -4 into the equation y = mx + b to get the final equation of the line:

y = 3x - 4