Question

2. A line goes through the points (7,8) and (3, 10).

Answer 1

1.

The formula of a slope (m):

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

We have the points (7, 8) and (3, 10). Substitute:

$m=\dfrac{10-8}{3-7}=\dfrac{2}{-4}=-\dfrac{1}{2}$

2.

a) point-slope form:

$y-y_1=m(x-x_1)$

Substitute:

$y-8=-\dfrac{1}{2}(x-7)$

b) slope-intercept form:

$y=mx+b$

$y-8=-\dfrac{1}{2}(x-7)\qquad|\text{use distributive property}\\\\y-8=-\dfrac{1}{2}x+\dfrac{7}{2}\qquad|\text{add 8}=\dfrac{16}{2}\ \text{to both sides}\\\\y=-\dfrac{1}{2}x+\dfrac{23}{2}$