Final answer:
To find the equation of the line in slope-intercept form, we use the given slope (5) and the point (-6, 3) to calculate the y-intercept (b). After substituting the values into the formula y = mx + b, we determine that b = 33, thus the correct equation is y = 5x + 33. However, this option is not provided in the given choices.
Step-by-step explanation:
To find the equation of a line in slope-intercept form, which is y = mx + b, where m is the slope and b is the y-intercept, first, we know the slope (m) is 5. We also have a point on the line, (-6, 3). Using the slope-intercept form, we can substitute the known values to find b:
y = mx + b
3 = 5(-6) + b
3 = -30 + b
b = 3 + 30
b = 33
Therefore, the equation of the line is:
y = 5x + 33
However, looking at the options provided, there seems to be a mistake because none of the options match the correct equation y = 5x + 33. All the given options have incorrect y-intercepts given the slope of 5 and the point (-6, 3).