Let's organize.
The question says to identify an equation in point-intercept form for the line that's parallel to y = -3x + 7 that passes through (2, -4).
If you need to find an equation in point-intercept form that passes through a point, you will substitute the coordinate in this formula:
-> y - yo = m (x - xo)
Where:
(2, -4) -> xo = 2 ; yo = -4
m = Slope
You don't have the slope, but you have the information that the line is parallel to y = -3x + 7. Then you need to know that to a line be parallel to another the Slopes of each other must be equal, mr = ms.
Let's find the slope of the equation given, it is in a slope-intercept form, so:
y = mx + b
R: y = -3x + 7 // I will call this one R line, and the other S.
mr = -3
If the mr = ms, and mr = -3, then the ms = -3 too.
S: y - yo = ms (x - xo) // (2, -4) & ms = -3
-> y - (-4) = -3 (x - 2)
-> S: y + 4 = -3 (x - 2) -> This is the point-slope form.
-> y = -3x + 6 - 4
-> S: y = -3x - 2 -> This is the slope-intercept form.
I didn't understand what is the point-intercept form that the question requests, but by logic, i think that's the point-slope form.
Answer: The equation in point-intercept form is: y + 4 = -3 (x - 2).