Step-by-step explanation:
first we need to calculate the slope, which is needed in both equation forms.
the slope is the ratio "y coordinate change / x coordinate change" when going from one point on the line to another.
I always prefer to go from left to right (but it works exactly the same way in the opposite direction), so I go from (-1, 3) to (7, -4).
x changes by +8 (from -1 to +7).
y changes by -7 (from +3 to -4).
so, the slope is -7/+8 = -7/8
when (7, -4) is used (I think you have a typo in the problem description up there), the point-slope form is
y - y1 = m(x - x1)
with (x1, y1) being the point coordinates, and m bring the slope
y - -4 = -7/8 × (x - 7)
or simplified
y + 4 = -7/8(x - 7)
the slope-intercept form is
y = mx + n
m being the slope, n being the y-intercept (y value for x=0).
we know already
y = -7/8 x + n
we also use the coordinates of a point here to solve for n :
-4 = -7/8 × 7 + n = -49/8 + n
-32/8 = -49/8 + n
17/8 = n
so, the full equation is
y = -7/8 x + 17/8
