Question: Find the slope and the y-intercept of the line. y = 3/4 - 5/4 x slope: y-intercept: 3/4 Graph shape: a linear equation is shown, y = 3/4 - 5/4 x, with slope -5/4 and y-intercept 3/4; position_hint = center Find the slope of the line graphed below. Graph: a coordinate plane with a line rising left to right through the points (0, -3) and (2, 4), located in the center-left. Slope = 7/2

1. **State the problem:** We need to find the slope and y-intercept of the line given by the equation $$y = \frac{3}{4} - \frac{5}{4}x$$ and also find the slope of the line passing through points $(0, -3)$ and $(2, 4)$. 2. **Rewrite the equation in slope-intercept form:** The slope-intercept form is $$y = mx + b$$ where $m$ is the slope and $b$ is the y-intercept. 3. **Identify slope and y-intercept from the first equation:** Given $$y = \frac{3}{4} - \frac{5}{4}x$$ we rewrite it as $$y = -\frac{5}{4}x + \frac{3}{4}$$. - The slope $m = -\frac{5}{4}$. - The y-intercept $b = \frac{3}{4}$. 4. **Find the slope of the line through points $(0, -3)$ and $(2, 4)$:** Use the slope formula $$m = \frac{y_2 - y_1}{x_2 - x_1}$$ where $(x_1, y_1) = (0, -3)$ and $(x_2, y_2) = (2, 4)$. 5. **Calculate the slope:** $$m = \frac{4 - (-3)}{2 - 0} = \frac{4 + 3}{2} = \frac{7}{2}$$ 6. **Final answers:** - Slope of the first line: $$-\frac{5}{4}$$ - Y-intercept of the first line: $$\frac{3}{4}$$ - Slope of the line through the points: $$\frac{7}{2}$$