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How do you write the equation of the line in standard form through 4 and 2 and -4 and -2?
Let (x1, y1) = (-4, -2) and (x2, y2) = (4, 2), then the slope m of the line is:
m = (y2 - y1)/(x2 - x1) = [2 - (-2)]/[4 - (-4)] = (2 + 2)/(4 + 4) = 4/8 = 1/2
Write the point-slope form of the equation of a line by using the slope m = 1/2 and the point (4, 2):
(y - y2) = m(x - x2) substitute what you know into the equation
(y - 2) = (1/2)(x - 4)
y - 2 = (1/2)x - 2 subtract (1/2)x and add 2 to both sides
y - (1/2)x = 0 multiply by -1 to both sides and interchange the places of the terms
(1/2)x - y = 0
Thus, the standard form (Ax + By = C) is (1/2)x - y = 0.
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