Questions: Are the two lines parallel, perpendicular, or neither? Choose one · 1 point

Transcript text: Are the two lines parallel, perpendicular, or neither? Choose one $\cdot$ 1 point

Solution

Solution Steps

Step 1: Identify the slopes of the lines

To determine if the lines are parallel, perpendicular, or neither, we first need to identify the slopes of the two lines. The slope of a line in the form $ y = mx + b $ is given by $ m $.

Step 2: Determine the slope of the blue line

From the graph, the blue line passes through the points $(0, 5)$ and $(5, 10)$. The slope $ m $ is calculated as: \[ m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{10 - 5}{5 - 0} = \frac{5}{5} = 1 \]

Step 3: Determine the slope of the red line

From the graph, the red line passes through the points $(0, -5)$ and $(5, 0)$. The slope $ m $ is calculated as: \[ m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{0 - (-5)}{5 - 0} = \frac{5}{5} = 1 \]

Step 4: Compare the slopes

Since both lines have the same slope $ m = 1 $, they are parallel.