he equation of the line that passes through the points (0,2) and (1,5) is:

Step 1: Find the slope (m) of the line. The formula for the slope when given two points, (x1, y1) and (x2, y2), is m = (y2 - y1) / (x2 - x1).

Substitute the given points into the formula: m = (5 - 2) / (1 - 0) = 3.

Step 2: Use the slope-intercept form of a line, y = mx + b, where m is the slope and b is the y-intercept.

We already know that m = 3. The y-intercept (b) is the y-coordinate where the line crosses the y-axis. Since the line passes through (0,2), the y-intercept is 2.

Step 3: Substitute m and b into the slope-intercept equation: y = 3x + 2.

So, the equation of the line that passes through the points (0,2) and (1,5) is y = 3x + 2.