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 - line property

Parallel lines have equal slopes. The given line has a slope of 3.

Step2: Calculate slopes of given lines

For a line passing through two points $(x_1,y_1)$ and $(x_2,y_2)$, the slope $m=\frac{y_2 - y_1}{x_2 - x_1}$.
For line AB: It is a horizontal line, slope $m_{AB}=0$.
For line CD: Let's assume two points on line CD, say $(x_1,y_1)$ and $(x_2,y_2)$. If we count the rise and run, the rise is 2 and the run is 2, so $m_{CD}=\frac{2}{2}=1$.
For line FG: Let's assume two points on line FG. If we count the rise and run, the rise is - 2 and the run is 2, so $m_{FG}=\frac{-2}{2}=-1$.
For line HJ: If we count the rise and run for two points on line HJ, say starting from one point and moving to another, the rise is 3 and the run is 1. So $m_{HJ}=\frac{3}{1}=3$.

Answer:

line HJ