Question

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

Explanation:

Step1: Recall parallel lines property

Parallel lines have the same slope. The given line has a slope of 3. So we need to find the line in the graph with slope 3.

Step2: Analyze each line

• Line AB: Horizontal line, slope = 0 (since \(y\) - value is constant), not 3.
• Line CD: Let's find its slope. Take two points, say \((-3,0)\) and \((3,2)\). Slope \(m=\frac{2 - 0}{3-(-3)}=\frac{2}{6}=\frac{1}{3}\), not 3.
• Line FG: Let's find its slope. Take two points, say \((-1,-2)\) and \((2,7)\)? Wait, no, looking at the red line (HJ? Wait, the red line is HJ? Wait, the red line has a steep slope. Wait, let's check the red line (HJ? Wait, the line with slope 3: let's see the red line. Let's take two points on the red line, say \((0, - 3)\) and \((1,0)\)? No, wait, the given line has slope 3, so \(y = 3x+3\). The red line (HJ? Wait, the line HJ: let's check its slope. Wait, maybe I mislabeled. Wait, the red line: let's take two points. Suppose it goes through \((0, - 3)\) and \((1,0)\), slope is \(\frac{0 - (-3)}{1-0}=3\). Wait, line HJ: let's check the options. The options are line AB, CD, FG, HJ. So line HJ has slope 3, so it's parallel to the line with slope 3.

Answer:

line HJ