How do you write an equation of a line that contains the points (-2,-5) and (3,5)?

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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!