Final answer:
The line that is parallel to y = -3x + 7 and passes through (-2, 2) will have the same slope of -3. Using point-slope form and solving for y-intercept, the equation of this line is found to be y = -3x - 4.
Step-by-step explanation:
The student is asking us to write the slope intercept form of an equation for the line that passes through a given point (-2, 2) and is parallel to the equation y=-3x+7. To do this, we must use the slope of the given line, which is -3, because parallel lines have the same slope. Next, we will use the slope (-3) and the given point (-2, 2) to solve for the y-intercept (b) of our new line.
Using the point-slope form:
y - y1 = m(x - x1)
y - 2 = -3(x - (-2))
y - 2 = -3(x + 2)
y - 2 = -3x - 6
y = -3x - 6 + 2
y = -3x - 4
Therefore, the slope-intercept form of the equation for our line is y = -3x - 4, so the correct answer is option A.