Identify an equation in point-intercept form for the line parallel to y = -3x + 7 that passes through (2, -4)

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.

The equation in point-intercept form is: y + 4 = -3 (x - 2).