Question

On a coordinate plane, 4 lines are shown. Line A B goes through (negative 4, 3) and (4, 3). Line C D goes through (negative 3, 0) and (3, 2). Line F G goes through (negative 3, negative 1) and (3, negative 3). Line H J goes through (negative 1, negative 4) and (1, 2).
Which of the lines that appear in the graph would be parallel to a line with a slope of 3 and a y-intercept at (0, 3)?

line AB
line CD
line FG
line HJ

Answer 1

To determine which of the given lines are parallel to a line with a slope of 3 and a y-intercept of (0, 3), we need to find the slope of each line.

1. **Line AB:**
- This line goes through the points (-4, 3) and (4, 3).
- The slope (m) is calculated as:

\[
m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{3 - 3}{4 - (-4)} = \frac{0}{8} = 0
\]

2. **Line CD:**
- This line goes through the points (-3, 0) and (3, 2).
- The slope (m) is calculated as:

\[
m = \frac{2 - 0}{3 - (-3)} = \frac{2}{3 + 3} = \frac{2}{6} = \frac{1}{3}
\]

3. **Line FG:**
- This line goes through the points (-3, -1) and (3, -3).
- The slope (m) is calculated as:

\[
m = \frac{-3 - (-1)}{3 - (-3)} = \frac{-3 + 1}{3 + 3} = \frac{-2}{6} = -\frac{1}{3}
\]

4. **Line HJ:**
- This line goes through the points (-1, -4) and (1, 2).
- The slope (m) is calculated as:

\[
m = \frac{2 - (-4)}{1 - (-1)} = \frac{2 + 4}{1 + 1} = \frac{6}{2} = 3
\]

Now, we compare the slopes:

- Line AB has a slope of 0.
- Line CD has a slope of \(\frac{1}{3}\).
- Line FG has a slope of \(-\frac{1}{3}\).
- Line HJ has a slope of 3.

The line with a slope of 3 and a y-intercept of (0, 3) has a slope of 3. Thus, Line HJ, which also has a slope of 3, is parallel to that line.

**Answer: Line HJ**