Question

12.
Are the graphs of the lines in the pair parallel? Explain.

y = 4x + 6
–15x + 3y = –45

Answer 1

To determine if the graphs of the lines are parallel, we need to compare their slopes. Lines are parallel if they have the same slope.

1. The first line is already in slope-intercept form (y = mx + b):
\[ y = 4x + 6 \]
Here, the slope (m) is \(4\).

2. For the second line, we need to rewrite the equation \(–15x + 3y = –45\) in slope-intercept form (y = mx + b).
We can solve for \(y\):
\[
3y = 15x - 45 \quad \text{(adding 15x to both sides)}
\]
\[
y = 5x - 15 \quad \text{(dividing all terms by 3)}
\]
Here, the slope (m) is \(5\).

3. Now, we compare the slopes of both lines:
- The first line has a slope of \(4\).
- The second line has a slope of \(5\).

Since the slopes \(4\) and \(5\) are not equal, the two lines are **not parallel**.