1. **Compute the slope between two points**: The slope formula is given by $$m = \frac{y_2 - y_1}{x_2 - x_1}$$ where $(x_1,y_1)$ and $(x_2,y_2)$ are the coordinates of the two points. 2. **Calculate slopes for each pair:** - For points $(2,4)$ and $(4,2)$: $$m = \frac{2 - 4}{4 - 2} = \frac{-2}{2} = -1$$ - For points $(12,8)$ and $(9,5)$: $$m = \frac{5 - 8}{9 - 12} = \frac{-3}{-3} = 1$$ - For points $(-2,-4)$ and $(2,8)$: $$m = \frac{8 - (-4)}{2 - (-2)} = \frac{12}{4} = 3$$ 3. **Identify the equation of lines from points:** - For the first graph with points approximately $(1,3)$ and $(4,1)$: Calculate slope: $$m = \frac{1 - 3}{4 - 1} = \frac{-2}{3} = -\frac{2}{3}$$ Use point-slope form $y - y_1 = m(x - x_1)$ with point $(1,3)$: $$y - 3 = -\frac{2}{3}(x - 1)$$ Simplify to slope-intercept form: $$y = -\frac{2}{3}x + \frac{2}{3} + 3 = -\frac{2}{3}x + \frac{11}{3}$$ - For the second graph with points approximately $(-3,-2)$ and $(2,1)$: Calculate slope: $$m = \frac{1 - (-2)}{2 - (-3)} = \frac{3}{5}$$ Use point-slope form with point $(-3,-2)$: $$y + 2 = \frac{3}{5}(x + 3)$$ Simplify: $$y = \frac{3}{5}x + \frac{9}{5} - 2 = \frac{3}{5}x - \frac{1}{5}$$ 4. **Graphing lines:** - $y = x - 3$ - $y = -2x + 4$ - $y = \frac{3}{4}x - 4$ - $y = \frac{5}{2}x$ These are linear equations in slope-intercept form $y = mx + b$, where $m$ is the slope and $b$ is the y-intercept. Plotting involves marking the y-intercept on the y-axis and using the slope to find other points. **Final answers:** - Slopes: $-1$, $1$, $3$ - Equations: 1. $y = -\frac{2}{3}x + \frac{11}{3}$ 2. $y = \frac{3}{5}x - \frac{1}{5}$ - Graph lines as given.