Question

Write an equation in slope intercept form for a line contains the points (1/2, -3/4) and (2/3, -7/4)

Answer 1

$y = mx + b\\y(\frac{1}{2}) = \frac{1}{2}m + b = -\frac{3}{4}\\y(\frac{2}{3}) = \frac{2}{3}m + b = -\frac{7}{4}\\\\2m + 4b = -3|\cdot(-4)\\8m + 12b = -21\\\\-8m - 16b = 12\\8m + 12b = -21\\-4b  = -9 => b = \frac{9}{4}\\2m + 4(\frac{9}{4}) = -3\\2m + 9 = -3\\m = -6 => y = -6x + \frac{9}{4}$