Question: User: 8. Directions
Plot each exact point on the coordinate grid. A line will connect the points.
Graph the line represented by the equation $y = \frac{7}{3} x - 2$.
Select TWO points on the coordinate grid. A line will connect the points.
Graph shape: coordinate grid with x- and y-axes crossing at the center, pink arrowed axes extending in all four directions; the line to graph is $y = \frac{7}{3} x - 2$, which has y-intercept at $(0, -2)$ and rises 7 for every 3 to the right. position_hint = center
1. **State the problem:** We need to graph the line given by the equation $$y = \frac{7}{3} x - 2$$ on a coordinate grid.
2. **Identify key components:** The equation is in slope-intercept form $$y = mx + b$$ where $$m = \frac{7}{3}$$ is the slope and $$b = -2$$ is the y-intercept.
3. **Plot the y-intercept:** The y-intercept is the point where the line crosses the y-axis, at $$x=0$$. So plot the point $$(0, -2)$$.
4. **Use the slope to find another point:** The slope $$\frac{7}{3}$$ means "rise over run" = rise 7 units up for every 3 units right.
5. **Calculate the second point:** Starting from $$(0, -2)$$, move 3 units to the right (x increases by 3) and 7 units up (y increases by 7):
$$
(0 + 3, -2 + 7) = (3, 5)
$$
Plot the point $$(3, 5)$$.
6. **Draw the line:** Connect the points $$(0, -2)$$ and $$(3, 5)$$ with a straight line extending in both directions.
7. **Verify with a third point (optional):** For example, at $$x = 6$$:
$$
y = \frac{7}{3} \times 6 - 2 = 14 - 2 = 12
$$
So the point $$(6, 12)$$ lies on the line, confirming the slope.
**Final answer:** The line passes through points $$(0, -2)$$ and $$(3, 5)$$ with slope $$\frac{7}{3}$$.