Question

which graph best represents -5y = -6x + 15?

Explanation:

Step1: Rewrite in slope - intercept form

First, solve the equation $- 5y=-6x + 15$ for $y$. Divide each term by $-5$: $y=\frac{-6x}{-5}+\frac{15}{-5}$, which simplifies to $y=\frac{6}{5}x - 3$.

Step2: Analyze slope and y - intercept

The slope $m=\frac{6}{5}>0$, so the line is increasing. The y - intercept $b=-3$, which means the line crosses the y - axis at the point $(0,-3)$.

Answer:

The graph with a positive - slope and y - intercept of $(0, - 3)$ (assuming graph C has these characteristics among the given options) is the correct one. Without specific coordinates on the graphs, we know it's a line with positive slope and y - intercept at $y =-3$. If graph C has a line that rises from left to right and crosses the y - axis at $y=-3$, then the answer is C.