Question

Line AB passes through points A(–6, 6) and B(12, 3). If the equation of the line is written in slope-intercept form, y = mx + b, then m = – and b = .

Answer 1

The formula of a slope:

$m=\dfrac{y_2-y_1}{x_2-x_1}$

We have the points A(-6, 6) and B(12, 3). Substitute:

$m=\dfrac{3-6}{12-(-6)}=\dfrac{-3}{18}=-\dfrac{3:3}{18:3}=-\dfrac{1}{6}$

Therefore we have $y=-\dfrac{1}{6}x+b$.

Put the coordinates of the point B to the equation:

$3=-\dfrac{1}{6}(12)+b$

$3=-2+b$          add 2 to both sides

$5=b\to b=5$

Answer:

$m=-\dfrac{1}{6}\\\\b=5$