Answer:
r = 1
Step-by-step explanation:
Calculate the slope m using the slope formula and equate to [tex]\frac{1}{2}[/tex]
m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
with (x₁, y₁ ) = (- 1, - 3) and (x₂, y₂ ) = (7, r)
m = [tex]\frac{r+3}{7+1}[/tex] = [tex]\frac{r+3}{8}[/tex] = [tex]\frac{1}{2}[/tex] ( cross- multiply )
2(r + 3) = 8 ← distribute left side
2r + 6 = 8 ( subtract 6 from both sides )
2r = 2 ( divide both sides by 2 )
r = 1
