Question

given the equation $y = -\frac{1}{3}x$, and a table with $x$ values -9, 0, 3, 6, 9, and a coordinate grid with a red line plotted. the table has corresponding $y$ values calculated (e.g., for $x=-9$, $y$ is calculated as $-\frac{1}{3}(-9)=3$; for $x = 0$, $y=-\frac{1}{3}(0)=0$; etc.).

Explanation:

Step1: Substitute $x=-9$ into equation

$y = -\frac{1}{3} \times (-9) = 3$

Step2: Substitute $x=0$ into equation

$y = -\frac{1}{3} \times 0 = 0$

Step3: Substitute $x=3$ into equation

$y = -\frac{1}{3} \times 3 = -1$

Step4: Substitute $x=6$ into equation

$y = -\frac{1}{3} \times 6 = -2$

Step5: Substitute $x=9$ into equation

$y = -\frac{1}{3} \times 9 = -3$

Answer:

The completed table is:

$x$	$y$
$0$	$0$
$3$	$-1$
$6$	$-2$
$9$	$-3$

The graphed line matches the linear function $y=-\frac{1}{3}x$, as it passes through all the calculated points.