Question

Write the equation of the line that passes through the points (-5, 9) and (-2, 1).
Put your answer in fully simplified point-slope form, unless it is a vertical or
horizontal line.

Answer 1

Answer:

$\displaystyle y=\frac{-8}{3}x-3\frac{2}{3}$

Step-by-step explanation:

        Slope-intercept form is y = mx + b. This is where m is the slope and b is the y-intercept.

        We will be writing a point-slope equation, then simplifying it into a slope-intercept form equation. First, we need to find the slope. We find that we have a slope of $\frac{-8}{3}$.

$\displaystyle \frac{y_{2} -y_{1} }{x_{2} -x_{1} }=\frac{1-9}{-2--5} =\frac{-8}{3}$

        Next, we will write the point-slope equation.

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

y - 9 = $\frac{-8}{3}$(x - -5)

y - 9 = $\frac{-8}{3}$(x + 5)

y - 9 = $\frac{-8}{3}$x - 13$\frac{1}{3}$

y = $\frac{-8}{3}$x - 3 $\frac{2}{3}$