precalc problem

Question

Give the standard form of the equation of the line that contains the points ( -3/2 , -9 ) and ( 8 , 8/3 )

Answer 1

First, find the slope of the line: m = (8/3 - (-9))/(8 - (-3/2)) = 70/57. Using the slope-intercept form y = mx + b, we have y = (70/57)x + b. To find b, we may plug in x = -3/2 and y = -9 in the equation (since the line passes through the point (-3/2, -9)) to obtain -9 = (70/57)(-3/2) + b, or -9 = -35/19 + b, i.e., b = 408/57. Thus y = (70/57)x - 408/57. Multiplying by 57, 57y = 70x - 408. Rearranging the equation, 70x - 57y = 408. This is the standard form of the equation of the line.