Final answer:
The equation of the line that passes through the points (2,15) and (5,21) is y = 2x + 11.
Step-by-step explanation:
To write an equation in slope-intercept form, we need to determine the slope and the y-intercept.
Step 1: Find the slope (m) using the formula:
m = (y2 - y1) / (x2 - x1)
Using the points (2,15) and (5,21), the slope is (21 - 15) / (5 - 2) = 6 / 3 = 2.
Step 2: Substitute the slope and one of the given points into the equation y = mx + b to solve for the y-intercept (b).
Substituting (2,15) and m = 2:
15 = 2(2) + b
15 = 4 + b
b = 15 - 4 = 11
Therefore, the equation of the line is y = 2x + 11.