Question

in the graph to the right, are lines ( l_1 ) and ( l_2 ) parallel? explain. choose the correct answer below
a. yes, lines ( l_1 ) and ( l_2 ) are parallel because they have different slopes.
b. no, lines ( l_1 ) and ( l_2 ) are not parallel because they have the same slope.
c. no, lines ( l_1 ) and ( l_2 ) are not parallel because they have different slopes.
d. yes, lines ( l_1 ) and ( l_2 ) are parallel because they have the same slope.
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Explanation:

Step1: Recall the slope formula

The slope \( m \) between two points \((x_1, y_1)\) and \((x_2, y_2)\) is given by \( m=\frac{y_2 - y_1}{x_2 - x_1} \).

Step2: Find slope of \( L_1 \)

Let's take two points on \( L_1 \). From the graph, assume points \((-8, -2)\) and \((-4, 0)\) (we can identify these from the grid).
Using the slope formula: \( m_{L_1}=\frac{0 - (-2)}{-4 - (-8)}=\frac{0 + 2}{-4 + 8}=\frac{2}{4}=\frac{1}{2} \).

Step3: Find slope of \( L_2 \)

Take two points on \( L_2 \), say \((0, 0)\) and \((4, 4)\) (from the grid).
Using the slope formula: \( m_{L_2}=\frac{4 - 0}{4 - 0}=\frac{4}{4} = 1 \).

Step4: Compare slopes

Since \( m_{L_1}=\frac{1}{2} \) and \( m_{L_2}=1 \), the slopes are different. Parallel lines have the same slope, so \( L_1 \) and \( L_2 \) are not parallel because they have different slopes.

Answer:

C. No, lines \( L_1 \) and \( L_2 \) are not parallel because they have different slopes.