Line Slope Points D633F8

1. **State the problem:** We are given the linear equation $$y=\frac{2}{3}x-4$$ and two points $(0,-4)$ and $(3,-2)$ that lie on the graph. We want to understand the graph and verify the slope. 2. **Formula and slope:** The equation is in slope-intercept form $$y=mx+b$$ where $m$ is the slope and $b$ is the y-intercept. 3. **Identify slope and intercept:** Here, $$m=\frac{2}{3}$$ and $$b=-4$$. 4. **Check points:** - For $(0,-4)$, substitute $x=0$: $$y=\frac{2}{3}\times 0 -4 = -4$$ which matches the point. - For $(3,-2)$, substitute $x=3$: $$y=\frac{2}{3}\times 3 -4 = 2 -4 = -2$$ which matches the point. 5. **Slope verification:** The slope between the two points is $$m=\frac{y_2 - y_1}{x_2 - x_1} = \frac{-2 - (-4)}{3 - 0} = \frac{2}{3}$$ which matches the slope in the equation. 6. **Summary:** The line passes through the points $(0,-4)$ and $(3,-2)$ and has slope $\frac{2}{3}$, consistent with the equation. 7. **Graph description:** The line crosses the y-axis at $-4$ and rises $2$ units for every $3$ units it moves to the right. **Final answer:** The equation $$y=\frac{2}{3}x -4$$ correctly represents the line through the points $(0,-4)$ and $(3,-2)$ with slope $\frac{2}{3}$.