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. \

$$\begin{tabular}{|c|c|} \\hline x & y \\\\ \\hline \\boxed{} & 15 \\\\ \\hline -6 & \\boxed{} \\\\ \\hline \\boxed{} & 5 \\\\ \\hline 15 & \\boxed{} \\\\ \\hline \\end{tabular}$$

Explanation:

Step1: Find x when y=15

Given \( y = -\frac{2}{3}x + 7 \), substitute \( y = 15 \):
\( 15 = -\frac{2}{3}x + 7 \)
Subtract 7: \( 8 = -\frac{2}{3}x \)
Multiply 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 \( y = 5 \):
\( 5 = -\frac{2}{3}x + 7 \)
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 \( x = 15 \):
\( y = -\frac{2}{3}(15) + 7 = -10 + 7 = -3 \)

Answer:

x	y
-6	11
3	5
15	-3

(The boxes should be filled with -12, 11, 3, -3 respectively from top to bottom in the x or y columns as per the table structure.)