Respuesta :

Answer:

r = 7

Step-by-step explanation:

Calculate the slope using the slope formula then equate to - [tex]\frac{1}{4}[/tex]

m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]

with (x₁, y₁ ) = (- 6, r ) and (x₂, y₂ ) = (2, 5 )

m = [tex]\frac{5-r}{2-(-6)}[/tex] = [tex]\frac{5-r}{2+6}[/tex] = [tex]\frac{5-r}{8}[/tex] , then

[tex]\frac{5-r}{8}[/tex] = - [tex]\frac{1}{4}[/tex] ( multiply both sides by 8 to clear the fractions )

5 - r = - 2 ( subtract 5 from both sides )

- r = - 7 ( multiply both sides by - 1 )

r = 7

BasketballEinstein

Answer:

[tex]\displaystyle 7[/tex]

Step-by-step explanation:

[tex]\displaystyle \frac{-y_1 + y_2}{-x_1 + x_2} = m\\ \\ \frac{-r + 5}{6 + 2} = m \Rightarrow \frac{-r + 5}{8} \hookrightarrow -\frac{2}{8} = -\frac{1}{4} \\ \\ \boxed{7 = r}[/tex]

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