Sovi.AI - AI Math Tutor

Scan to solve math questions

QUESTION IMAGE

2 $y = 1 - \\frac{x}{3}$ | $x$ | $y$ | | --- | --- | | -6 | $1 - \\frac…

Question

2
$y = 1 - \frac{x}{3}$

$x$$y$
-3$1 - \frac{-3}{3} = 1 + 1 = 2$
0$1 - 0 = 1$
3$1 - \frac{3}{3} = 1 - 1 = 0$
6$1 - \frac{6}{3} = 1 - 2 = -1$

(there is also a coordinate grid for graphing the function.)

Explanation:

Step1: Calculate y for x=-6

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

Step2: Calculate y for x=-3

Substitute $x=-3$ into $y=1-\frac{x}{3}$:
$y=1-\frac{-3}{3}=1+1=2$

Step3: Calculate y for x=0

Substitute $x=0$ into $y=1-\frac{x}{3}$:
$y=1-\frac{0}{3}=1-0=1$

Step4: Calculate y for x=3

Substitute $x=3$ into $y=1-\frac{x}{3}$:
$y=1-\frac{3}{3}=1-1=0$

Step5: Calculate y for x=6

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

Step6: List valid (x,y) pairs

The corrected coordinate pairs are:
$(-6, 3), (-3, 2), (0, 1), (3, 0), (6, -1)$
These points are plotted on the grid by marking each (x,y) location and drawing a straight line through them.

Answer:

Corrected table values:

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

The graph is a straight line passing through the points listed above.