Question

type the correct answer in each box. use numerals instead of words. the domain of this function is {-12, -6, 3, 15}. y = -\frac{2}{3}x + 7 complete the table based on the given domain. x | y \boxed{} | 15 -6 | \boxed{} \boxed{} | 5 15 | \boxed{}

Explanation:

Step1: Find x when y = 15

We have the equation \( y = -\frac{2}{3}x + 7 \). Substitute \( y = 15 \):
\( 15 = -\frac{2}{3}x + 7 \)
Subtract 7 from both sides: \( 8 = -\frac{2}{3}x \)
Multiply both sides by \( -\frac{3}{2} \): \( x = 8 \times (-\frac{3}{2}) = -12 \)

Step2: Find y when x = -6

Substitute \( x = -6 \) into \( y = -\frac{2}{3}x + 7 \):
\( y = -\frac{2}{3}(-6) + 7 = 4 + 7 = 11 \)

Step3: Find x when y = 5

Substitute \( y = 5 \) into \( y = -\frac{2}{3}x + 7 \):
\( 5 = -\frac{2}{3}x + 7 \)
Subtract 7: \( -2 = -\frac{2}{3}x \)
Multiply by \( -\frac{3}{2} \): \( x = (-2) \times (-\frac{3}{2}) = 3 \)

Step4: Find y when x = 15

Substitute \( x = 15 \) into \( y = -\frac{2}{3}x + 7 \):
\( y = -\frac{2}{3}(15) + 7 = -10 + 7 = -3 \)

Answer:

First box (x when y=15): -12
Second box (y when x=-6): 11
Third box (x when y=5): 3
Fourth box (y when x=15): -3