Question

graph the line.
$y = -\frac{1}{3}x + 6$

Explanation:

Step1: Find y-intercept (x=0)

Substitute $x=0$ into $y=-\frac{1}{3}x+6$:
$y=-\frac{1}{3}(0)+6=6$
Point: $(0, 6)$

Step2: Find x-intercept (y=0)

Set $y=0$, solve for $x$:
$0=-\frac{1}{3}x+6$
$\frac{1}{3}x=6$
$x=18$? No, correction: $x=6\times3=18$? Wait no, $0=-\frac{1}{3}x+6$ → $\frac{1}{3}x=6$ → $x=18$? Wait no, alternative point: let $x=3$
$y=-\frac{1}{3}(3)+6=-1+6=5$, point $(3,5)$; or $x=9$: $y=-\frac{1}{3}(9)+6=-3+6=3$, point $(9,3)$; wait x-intercept is when y=0: $0=-\frac{1}{3}x+6$ → $\frac{1}{3}x=6$ → $x=18$, but 18 is off the given grid. So use (0,6) and (9,3), or (0,6) and (3,5).

Step3: Plot points and draw line

Plot $(0, 6)$ (on y-axis) and $(9, 3)$ (or $(3,5)$), then draw a straight line through them to represent $y=-\frac{1}{3}x+6$.

Wait correction for x-intercept: $0=-\frac{1}{3}x+6$ → $\frac{1}{3}x=6$ → $x=18$, which is outside the grid shown (x goes to 10). So better to use (0,6) and (6,4): $y=-\frac{1}{3}(6)+6=-2+6=4$, point (6,4). Both (0,6) and (6,4) are within the grid.

Revised Step2: Find a second grid point
Substitute $x=6$ into $y=-\frac{1}{3}x+6$:
$y=-\frac{1}{3}(6)+6=-2+6=4$
Point: $(6, 4)$

Step3: Plot and connect points

Plot $(0, 6)$ and $(6, 4)$, then draw a straight line through these points, extending it across the visible grid.

Answer:

The line passes through points (0, 6) and (9, 0), and connects them to form the graph of $y=-\frac{1}{3}x+6$.