We have the function:
[tex]y=-\frac{2}{3}x+7[/tex]When we have the value of x, and we want to find the value of y, we replace x in the equation and calculate.
For x=-6, we have:
[tex]y=-\frac{2}{3}\cdot(-6)+7=\frac{-2\cdot6}{3}+7=-\frac{12}{3}+7=-4+7=3[/tex]The value of y for x=-6 is y=3.
When we know y, and we want to know the value of x, we replace y and calculate.
For y=5, we have:
[tex]\begin{gathered} 5=-\frac{2}{3}x+7 \\ 5-7=-\frac{2}{3}x \\ -2=-\frac{2}{3}x \\ x=-2\cdot(-\frac{3}{2})=\frac{2\cdot3}{2}=3 \end{gathered}[/tex]For y=5, the value of x is x=3.
We repeat this for the last two cases:
x=15, the value of y is y=17
[tex]y=-\frac{2}{3}(15)+7=10+7=17[/tex]y=15, the value of x is x=-12
[tex]\begin{gathered} 15=-\frac{2}{3}x+7 \\ 15-7=-\frac{2}{3}x \\ 8=-\frac{2}{3}x \\ 8\cdot3=-2x \\ 24=-2x \\ x=\frac{24}{-2}=-12 \end{gathered}[/tex]
