1. **State the problem:** We need to find the y-intercept and slope of the line given by the equation $$-3y = 15 - 4x$$ and identify which line (A, B, C, or D) represents this equation on the graph. 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. Starting with: $$-3y = 15 - 4x$$ Divide both sides by $$-3$$: $$y = \frac{15 - 4x}{-3}$$ Rewrite the fraction: $$y = \frac{15}{-3} - \frac{4x}{-3}$$ Simplify each term: $$y = -5 + \frac{4}{3}x$$ Or equivalently: $$y = \frac{4}{3}x - 5$$ 3. **Identify slope and y-intercept:** - The slope $$m = \frac{4}{3}$$ (positive slope) - The y-intercept $$b = -5$$ 4. **Match the line on the graph:** - The line must have a positive slope (so lines A, B, and D are candidates). - The y-intercept is at $$-5$$, which means the line crosses the y-axis at $$-5$$. - Line D crosses the y-axis at 5, so it is not correct. - Line B passes through (3,1), check if it fits the equation: $$y = \frac{4}{3} \times 3 - 5 = 4 - 5 = -1$$, but point is (3,1), so no. - Line A has a positive slope and presumably crosses y at -5, so line A matches. **Final answers:** - The y-intercept is $$-5$$. - The slope is $$\frac{4}{3}$$. - Line A is the graph of the line $$-3y = 15 - 4x$$.