Question

which graph represents $2x - 5y < 15$?

Explanation:

Step1: Rewrite in slope-intercept form

Rearrange $2x - 5y < 15$ to solve for $y$:
$-5y < -2x + 15$
Divide by $-5$ (reverse inequality sign):
$y > \frac{2}{5}x - 3$

Step2: Identify line properties

The boundary line is $y = \frac{2}{5}x - 3$, which has a slope of $\frac{2}{5}$ and y-intercept $-3$. Since the inequality is $>$, the line is dashed, and we shade above the line.

Step3: Match to the graph

• The line with y-intercept $-3$ and slope $\frac{2}{5}$ (rises 2, runs 5) is the second graph. The shading is above this dashed line, which matches $y > \frac{2}{5}x - 3$.

Answer:

The correct graph is the middle one (second square): dashed line with y-intercept -3, slope $\frac{2}{5}$, and shading above the line.