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.

Respuesta :

Answer:

[tex]\displaystyle y=\frac{-8}{3}x-3\frac{2}{3}[/tex]

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 [tex]\frac{-8}{3}[/tex].

[tex]\displaystyle \frac{y_{2} -y_{1} }{x_{2} -x_{1} }=\frac{1-9}{-2--5} =\frac{-8}{3}[/tex]

        Next, we will write the point-slope equation.

y - [tex]y_1[/tex] = m(x - [tex]x_1[/tex])

y - 9 = [tex]\frac{-8}{3}[/tex](x - -5)

y - 9 = [tex]\frac{-8}{3}[/tex](x + 5)

y - 9 = [tex]\frac{-8}{3}[/tex]x - 13[tex]\frac{1}{3}[/tex]

y = [tex]\frac{-8}{3}[/tex]x - 3 [tex]\frac{2}{3}[/tex]

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