Final answer:
The equation of the line with slope 3 passing through the point (5, -2) in slope-intercept form is y = 3x - 17.
Step-by-step explanation:
The equation of a line in slope-intercept form is y = mx + b, where m is the slope and b is the y-intercept. Since the slope is given as 3 and the line passes through the point (5, -2), we can substitute these values into the equation to find the y-intercept.
Using the formula y = mx + b, we have -2 = 3(5) + b. Solving for b, we get b = -17. Therefore, the equation of the line is y = 3x - 17.