Question

the line represented by the equation $3x + 5y = 2$ has a slope of $-\frac{3}{5}$. which shows the graph of this equation?

Explanation:

Step1: Rewrite to slope-intercept form

Start with the given equation:
$$3x + 5y = 2$$
Isolate $5y$:
$$5y = -3x + 2$$
Divide by 5:
$$y = -\frac{3}{5}x + \frac{2}{5}$$

Step2: Identify key line features

From $y = -\frac{3}{5}x + \frac{2}{5}$:

• Slope: $-\frac{3}{5}$ (line falls left to right)
• y-intercept: $\frac{2}{5}$ (crosses y-axis at $(0, 0.4)$, near the origin)

Step3: Match to graphs

1. First graph: Positive slope (rises left to right) → Eliminate.
2. Second graph: y-intercept near $(0,1)$, slope $-\frac{1}{2}$ (not $-\frac{3}{5}$) → Eliminate.
3. Third graph: Falls left to right, y-intercept near $(0,0.4)$, slope matches $-\frac{3}{5}$ → Correct.

Answer:

The third graph (rightmost one, with a downward-sloping line crossing the y-axis near (0, 0.4))