Question

4520va v. geometry sem a geometry slopes of parallel and perpendicular lines 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 cd line ab line hj line fg

Explanation:

Step1: Recall the slope - intercept form

The equation of a line in slope - intercept form is \(y = mx + b\), where \(m\) is the slope and \(b\) is the \(y\) - intercept. Given \(m = 3\) and \(b=3\), the equation of the line is \(y = 3x+3\). Parallel lines have the same slope.

Step2: Calculate the slopes of the given lines

• For line \(AB\): It is a horizontal line. The slope \(m_{AB}=\frac{y_2 - y_1}{x_2 - x_1}\), since \(y\) - values are constant (e.g., if \(A(x_1,y_1)\) and \(B(x_2,y_2)\) with \(y_1 = y_2 = 3\)), \(m_{AB}=0\).
• For line \(CD\): Let \(C(-3,0)\) and \(D(3,2)\). Using the slope formula \(m=\frac{y_2 - y_1}{x_2 - x_1}\), \(m_{CD}=\frac{2 - 0}{3-(-3)}=\frac{2}{6}=\frac{1}{3}\).
• For line \(HJ\): Let \(H(0,-4)\) and \(J(1, - 1)\). Using the slope formula \(m=\frac{y_2 - y_1}{x_2 - x_1}\), \(m_{HJ}=\frac{-1-(-4)}{1 - 0}=\frac{-1 + 4}{1}=3\).
• For line \(FG\): Let \(F(-2,-1)\) and \(G(4,-3)\). Using the slope formula \(m=\frac{y_2 - y_1}{x_2 - x_1}\), \(m_{FG}=\frac{-3-(-1)}{4-(-2)}=\frac{-3 + 1}{6}=-\frac{1}{3}\).

Answer:

line \(HJ\)