1. **State the problem:** We need to graph the line given by the equation $$y - 4 = -\frac{2}{3}(x - 1)$$ which is in point-slope form. 2. **Recall the formula:** The point-slope form of a line is $$y - y_1 = m(x - x_1)$$ where $m$ is the slope and $(x_1,y_1)$ is a point on the line. 3. **Identify slope and point:** Here, $m = -\frac{2}{3}$ and the point is $(1,4)$. 4. **Convert to slope-intercept form:** $$y - 4 = -\frac{2}{3}(x - 1)$$ $$y - 4 = -\frac{2}{3}x + \frac{2}{3}$$ $$y = -\frac{2}{3}x + \frac{2}{3} + 4$$ $$y = -\frac{2}{3}x + \frac{2}{3} + \frac{12}{3}$$ $$y = -\frac{2}{3}x + \frac{14}{3}$$ 5. **Find intercepts:** - **y-intercept:** Set $x=0$: $$y = -\frac{2}{3}(0) + \frac{14}{3} = \frac{14}{3} \approx 4.67$$ - **x-intercept:** Set $y=0$: $$0 = -\frac{2}{3}x + \frac{14}{3}$$ Multiply both sides by 3: $$0 = -2x + 14$$ Add $2x$ to both sides: $$2x = 14$$ Divide both sides by 2: $$x = \cancel{\frac{14}{2}} = 7$$ 6. **Plot points:** The line passes through $(1,4)$, $(0, \frac{14}{3})$, and $(7,0)$. 7. **Draw the line:** Connect these points with a straight line extending in both directions. **Final answer:** The line has slope $-\frac{2}{3}$ and y-intercept $\frac{14}{3}$. It passes through $(1,4)$ and $(7,0)$.