Question

Find the slope between the given points and write an equation in slope-intercept form. (-3, 5) and (-1, -3)

Answer 1

The slope (m) of the line that passes through the points (x1, y1) and (x2, y2) is computed as follows:

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

In this case, the line passes through the points (-3, 5) and (-1, -3), then its slope is:

$m=\frac{-3-5}{-1-(-3)}=\frac{-8}{2}=-4$

Equation of a line in slope-intercept form

y = mx + b

where m is the slope and b is the y-intercept.

Substituting with m = -4 and the point (-3, 5), that is, x = -3 and y = 5, and solving for b:

$\begin{gathered} 5=(-4)\cdot(-3)+b \\ 5=12+b \\ 5-12=12+b-12 \\ -7=b \end{gathered}$

Substituting m = -4 and b = -7 into the equation, we get:

y = -4x + (- 7)

y = -4x - 7