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=(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=(-3-5)/(-1-(-3))=(-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