A line that passes through both of these points will have the same slope, since two points actually define the unique line. Write two slope statements and set them equal:
[y-(-5)] / [x-(-2)] must equal (y-5) / (x-3) since both are statements of slope for the same line. The first one becomes (y+5) / (x+2) when the inner parentheses are removed.
Now multiply both sides by (x +2)
(y+5) = (y-5)(x+2) / (x-3) Now multiply both sides by (x-3)
(y+5)(x-3) = (y-5)(x+2) Use FOIL to expand both sides
xy +5x-3y-15 = xy-5x+2y-10 Gather like terms and subtract off xy from both sides
10x-5 = 5y or rearranged 5y = 10x-5
Divide both sides by 5
y = 2x-1 should be true for both points. check
-5 = -4-1 = -5 Yes!
5 = 6-1 = 5 Yes! So the solution above is correct.
Slope is the most important math idea you'll ever learn after ratio and proportion!