Respuesta :
To answer this question it is necessary to find the equation of the given lines
Find the equation for PQ. To do it, find the slope of the equation:
[tex]m=\frac{6-(-5)}{5-2}=\frac{11}{3}[/tex]Now, use the point slope formula to find the equation of the line:
[tex]\begin{gathered} y-6=\frac{11}{3}(x-5) \\ y=\frac{11}{3}x-\frac{55}{3}+6 \\ y=\frac{11}{3}x-\frac{37}{3} \end{gathered}[/tex]Parallel lines have the same slope, it means PQ and RS have the same slope, then RS has a slope of 11/3
Use the point slope formula to find the equation of the line RS:
[tex]\begin{gathered} y-(-1)=\frac{11}{3}(x-3) \\ y+1=\frac{11}{3}x-11 \\ y=\frac{11}{3}x-12 \end{gathered}[/tex]Now, use this equation to find y when x is 6 (which corresponds to point S):
[tex]\begin{gathered} y=\frac{11}{3}x-12 \\ y=\frac{11}{3}(6)-12 \\ y=22-12 \\ y=10 \end{gathered}[/tex]y has a value of 10.
