Final answer:
To determine the equation of the line with a given slope and point, we use the point-slope form and then rearrange the equation to find the y-intercept. The correct equation for a line with a slope of 3 passing through the point (-3,-2) is y = 3x + 7.
Step-by-step explanation:
The student has asked for the equation of the line with a slope of 3 that passes through the point (-3,-2). The general form of a linear equation is y = mx + b, where m is the slope and b is the y-intercept.
To find the correct equation, we use the point (-3, -2) and the slope of 3 in the slope-point form of a line equation: y - y₁ = m(x - x₁).
Substitute the known values: y - (-2) = 3(x - (-3)), simplifying this gives us y + 2 = 3x + 9. To find the y-intercept, rearrange the equation to the slope-intercept form (y = mx + b), giving us y = 3x + 7.
Therefore, the equation that describes the line is y = 3x + 7, which corresponds to option D.