Question

7.
Are the graphs of the lines in the pair parallel? Explain.

y =3/7 x + 11
–3x + 7y = 13

Answer 1

To determine if the two lines are parallel, we need to compare their slopes. Two lines are parallel if they have the same slope.

1. **Find the slope of the first line:**
The first line is given in slope-intercept form \( y = mx + b \):
\[
y = \frac{3}{7}x + 11
\]
Here, the slope \( m_1 \) is \( \frac{3}{7} \).

2. **Convert the second line to slope-intercept form:**
The second line is given as:
\[
-3x + 7y = 13
\]
We can rearrange this to solve for \( y \):
\[
7y = 3x + 13
\]
\[
y = \frac{3}{7}x + \frac{13}{7}
\]
Here, the slope \( m_2 \) is also \( \frac{3}{7} \).

3. **Compare the slopes:**
Since both lines have the same slope:
\[
m_1 = \frac{3}{7} \quad \text{and} \quad m_2 = \frac{3}{7}
\]

4. **Conclusion:**
Yes, the graphs of the lines in the pair are parallel because they have the same slope of \( \frac{3}{7} \).