Question

The line represented by the equation 3x + 5y = 2 has a slope of negative StartFraction 3 Over 5 EndFraction.. Which shows the graph of this equation?

A coordinate plane with a line passing through (negative 5, negative 4), (0, negative 1), and (3, 1).

A coordinate plane with a line passing through (negative 1, 1) and (4, negative 2).

A coordinate plane with a line passing through (0, 1) and (3, negative 4).

A coordinate plane with a line passing through (0, negative 2) and (1, 0).

Answer 1

To determine which graph corresponds to the equation \( 3x + 5y = 2 \), we need to find the slope and y-intercept of the line.

First, we can rearrange the equation into slope-intercept form (\( y = mx + b \)):

1. Start with the original equation:
\[
3x + 5y = 2
\]

2. Isolate \( y \) on one side:
\[
5y = -3x + 2
\]

3. Divide every term by 5:
\[
y = -\frac{3}{5}x + \frac{2}{5}
\]

From this, we see that the slope \( m \) is \( -\frac{3}{5} \) and the y-intercept \( b \) is \( \frac{2}{5} \).

### Now, let's analyze the given options:

1. **First option**: A line passing through (negative 5, negative 4), (0, negative 1), and (3, 1).
- Calculate the slope between the points (0, -1) and (3, 1):
\[
m = \frac{1 - (-1)}{3 - 0} = \frac{2}{3}
\]
- This slope does not match \( -\frac{3}{5} \).

2. **Second option**: A line passing through (negative 1, 1) and (4, negative 2).
- Calculate the slope:
\[
m = \frac{-2 - 1}{4 - (-1)} = \frac{-3}{5}
\]
- The slope matches \( -\frac{3}{5} \).

3. **Third option**: A line passing through (0, 1) and (3, negative 4).
- Calculate the slope:
\[
m = \frac{-4 - 1}{3 - 0} = \frac{-5}{3}
\]
- This slope does not match \( -\frac{3}{5} \).

4. **Fourth option**: A line passing through (0, negative 2) and (1, 0).
- Calculate the slope:
\[
m = \frac{0 - (-2)}{1 - 0} = \frac{2}{1} = 2
\]
- This slope does not match \( -\frac{3}{5} \).

### Conclusion
The only option that has a slope of \( -\frac{3}{5} \) is the **second option**, which shows the graph of the equation \( 3x + 5y = 2 \).