Answer:
x = 7
Step-by-step explanation:
since the points all lie on the same line then the slopes of adjacent points will have the same slope.
calculate the slope using R and S then equate to slope using R and T or S and T
calculate slope using slope formula
m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
with (x₁, y₁ ) = R (- 5, - 3 ) and (x₂, y₂ ) = S (- 1, - 1 )
[tex]m_{RS}[/tex] = [tex]\frac{-1-(-3)}{-1-(-5)}[/tex] = [tex]\frac{-1+3}{-1+5}[/tex] = [tex]\frac{2}{4}[/tex] = [tex]\frac{1}{2}[/tex]
Repeat with (x₁, y₁ ) = R (- 5, - 3 ) and (x₂, y₂ ) = T (x, 3 )
[tex]m_{RT}[/tex] = [tex]\frac{3-(-3)}{x-(-5)}[/tex] = [tex]\frac{3+3}{x+5}[/tex] = [tex]\frac{6}{x+5 }[/tex]
equating [tex]m_{RS}[/tex] and [tex]m_{RT}[/tex]
[tex]\frac{6}{x+5}[/tex] = [tex]\frac{1}{2}[/tex] ( cross- multiply )
x + 5 = 12 ( subtract 5 from both sides )
x = 7
