Question

graph this line using the slope and y-intercept:
$y = -\frac{7}{3}x + 6$
click to select points on the graph.

Explanation:

Step1: Identify y-intercept

The equation is in slope-intercept form $y=mx+b$, where $b$ is the y-intercept. Here, $b=6$, so the point is $(0, 6)$.

Step2: Use slope to find second point

Slope $m=-\frac{7}{3}=\frac{\text{rise}}{\text{run}}$. From $(0,6)$, move 3 units right (run=3) and 7 units down (rise=-7):
$x=0+3=3$, $y=6-7=-1$. The point is $(3, -1)$.

Step3: Use slope for third point

From $(3,-1)$, move 3 units right and 7 units down:
$x=3+3=6$, $y=-1-7=-8$. The point is $(6, -8)$.
Or move left 3, up 7 from $(0,6)$: $x=0-3=-3$, $y=6+7=13$ (off the given grid).

Answer:

1. Plot the y-intercept point $(0, 6)$ on the graph.
2. Plot the second point $(3, -1)$ on the graph.
3. Plot the third point $(6, -8)$ on the graph.
4. Draw a straight line connecting these three points to graph the line $y=-\frac{7}{3}x+6$.