Question

given the equation $y = 4 - \frac{1}{3}x$, there is a table with columns x and y (filled with red -3,5; 0,4; 3,3; 6,2; 9,1) and a coordinate grid with a red line graph.

Explanation:

Step1: Verify x=-3, solve for y

Substitute $x=-3$ into $y=4-\frac{1}{3}x$:
$y=4-\frac{1}{3}(-3)=4+1=5$

Step2: Verify x=0, solve for y

Substitute $x=0$ into $y=4-\frac{1}{3}x$:
$y=4-\frac{1}{3}(0)=4+0=4$

Step3: Verify x=3, solve for y

Substitute $x=3$ into $y=4-\frac{1}{3}x$:
$y=4-\frac{1}{3}(3)=4-1=3$

Step4: Verify x=6, solve for y

Substitute $x=6$ into $y=4-\frac{1}{3}x$:
$y=4-\frac{1}{3}(6)=4-2=2$

Step5: Verify x=9, solve for y

Substitute $x=9$ into $y=4-\frac{1}{3}x$:
$y=4-\frac{1}{3}(9)=4-3=1$

Step6: Confirm graph alignment

The calculated $(x,y)$ points $(-3,5), (0,4), (3,3), (6,2), (9,1)$ match the plotted points and the line on the coordinate grid.

Answer:

The table values are correct for the equation $y=4-\frac{1}{3}x$, and the plotted line accurately represents the linear function with the corresponding points:
$(-3,5), (0,4), (3,3), (6,2), (9,1)$