Final answer:
The correct equation of the line with slope m = 3 passing through the point (-5, 2) in slope-intercept form is y = 3x + 17, which corresponds to option a).
Step-by-step explanation:
The student is asking for the equation of a line with a given slope (m = 3) that passes through a specific point (-5, 2). The slope-intercept form of a line's equation is y = mx + b, where m is the slope and b is the y-intercept. To find b, we can plug the given point and slope into the equation:
2 = 3(-5) + b
2 = -15 + b
b = 2 + 15
b = 17
Now, we have both the slope and the y-intercept, so we can write the equation of the line as:
y = 3x + 17
Therefore, the correct choice is a) y = 3x + 17.