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 slope - parallel line relationship

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

Step2: Calculate slopes of lines in the graph

For line \(AB\): It is a horizontal line, slope \(m_{AB}=0\) (since \(y\) - value is constant for different \(x\) - values).
For line \(CD\): Using two - point formula \(m=\frac{y_2 - y_1}{x_2 - x_1}\), if \(C(- 3,0)\) and \(D(3,2)\), then \(m_{CD}=\frac{2 - 0}{3+3}=\frac{1}{3}\).
For line \(FG\): It is a non - vertical and non - horizontal line. If \(F(-2, - 1)\) and \(G(2,-3)\), then \(m_{FG}=\frac{-3 + 1}{2+2}=-\frac{1}{2}\).
For line \(HJ\): If \(H(-1,-4)\) and \(J(0,-1)\), then \(m_{HJ}=\frac{-1 + 4}{0 + 1}=3\).

Answer:

line HJ