Answer:
x + 2y = -2
Step-by-step explanation:
First, find the slope of the line that passes through (-4,7) and (2,4). As we move to the right from -4 to 2, x increases by 6, and y decreases by 3.
Thus, the slope of this given line is m = rise / run = -3/6, or -1/2.
Then a new line which is parallel to the given one must have the same slope: -1/2.
Starting with the slope-intercept form y = mx + b, we find the equation of the line through (4, -3) that is parallel to the line we just studied (above).
y = mx + b becomes -3 = (-1/2)(4) + b, or -3 = -2 + b. Then b = -1:
y = (-1/2)x - 1. We must put this into the form (Ax + By = C).
Multiply all terms of y = (-1/2)x - 1 by 2 to eliminate the fractional coefficient:
2y = -x - 2. Moving -x to the left side, we get:
x + 2y = -2
