Question

See attachment for question (I will report you if you are only doing it for the points)

Answer 1

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, $y = -\frac{2}{3}x + 7$, 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:

$y = -\frac{2}{3}(-6) + 7$

$y = -\frac{2}{1}(-2) + 7$

$y = 2 + 7$

$y = 9$

Find x when y = 5:

$5 = -\frac{2}{3}x + 7$

$5 - 7 = -\frac{2}{3}x + 7 - 7$

$-2 = -\frac{2}{3}x$

$-2 = \frac{-2x}{3}$

$-2*3 = \frac{-2x}{3}*3$

$-6 = -2x$

$\frac{-6}{-2} = \frac{-2x}{-2}$

$3 = x$

$x = 3$

Find y when x = 15:

$y = -\frac{2}{3}(15) + 7$

$y = -\frac{2}{1}(5) + 7$

$y = -10 + 7$

$y = -3$

Find x when y = 15:

$15 = -\frac{2}{3}x + 7$

$15 - 7 = -\frac{2}{3}x + 7 - 7$

$8 = -\frac{2}{3}x$

$8 = \frac{-2x}{3}$

$8*3 = \frac{-2x}{3}*3$

$24 = -2x$

$\frac{24}{-2} = \frac{-2x}{-2}$

$-12 = x$

$x = -12$