Answer:
x => y
-6 => 9
3 => 5
15 => -3
-12 => 15
Step-by-step explanation:
Given the domain function, {-12, -6, 3, 15}, and the equation of the function, [tex] y = -\frac{2}{3}x + 7 [/tex], we can complete the given table by simply plugging in the value of either x to find y, or y to find x in the table given. The domain values are all x-values you have in the table.
Find y when x = -6:
[tex] y = -\frac{2}{3}(-6) + 7 [/tex]
[tex] y = -\frac{2}{1}(-2) + 7 [/tex]
[tex] y = 2 + 7 [/tex]
[tex] y = 9 [/tex]
Find x when y = 5:
[tex] 5 = -\frac{2}{3}x + 7 [/tex]
[tex] 5 - 7 = -\frac{2}{3}x + 7 - 7 [/tex]
[tex] -2 = -\frac{2}{3}x [/tex]
[tex] -2 = \frac{-2x}{3} [/tex]
[tex] -2*3 = \frac{-2x}{3}*3 [/tex]
[tex] -6 = -2x [/tex]
[tex] \frac{-6}{-2} = \frac{-2x}{-2} [/tex]
[tex] 3 = x [/tex]
[tex] x = 3 [/tex]
Find y when x = 15:
[tex] y = -\frac{2}{3}(15) + 7 [/tex]
[tex] y = -\frac{2}{1}(5) + 7 [/tex]
[tex] y = -10 + 7 [/tex]
[tex] y = -3 [/tex]
Find x when y = 15:
[tex] 15 = -\frac{2}{3}x + 7 [/tex]
[tex] 15 - 7 = -\frac{2}{3}x + 7 - 7 [/tex]
[tex] 8 = -\frac{2}{3}x [/tex]
[tex] 8 = \frac{-2x}{3} [/tex]
[tex] 8*3 = \frac{-2x}{3}*3 [/tex]
[tex] 24 = -2x [/tex]
[tex] \frac{24}{-2} = \frac{-2x}{-2} [/tex]
[tex] -12 = x [/tex]
[tex] x = -12 [/tex]
