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Use the Slope and \( y \)-Intercept sliders to graph the line \( y=2 x-5 \). Click and drag the red point to \( (-4,2) \) Select Parallel and check the Show 2nd Line box to graph a line parallel to the given line. Compare the graphs and equations of each line, and find the slope of each line. Use the interactive figure to find your answer. Use the left and right arrow keys to move along a slider as needed. Click here to launch the interactive figure. The slope of the line \( y=2 x-5 \) is The slope of the parallel line through \( (-4,2) \) is

Ask by Chen Chang. in the United States
Mar 09,2025

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Tutor-Verified Answer

Answer

The slope of the line \( y=2x-5 \) is 2, and the slope of the parallel line through \( (-4,2) \) is also 2.

Solution

1. The equation of the given line is \( y=2x-5 \). In this equation, the coefficient of \( x \) is the slope. Therefore, the slope of the given line is \[ m = 2 \] 2. A line that is parallel to another line has the same slope as the given line. Therefore, the parallel line through \( (-4,2) \) also has the slope \[ m = 2. \] Thus, the slope of the line \( y=2x-5 \) is \( 2 \), and the slope of the parallel line through \( (-4,2) \) is also \( 2 \).

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Bonus Knowledge

The slope of the line \( y = 2x - 5 \) is 2. This means that for every one unit you move to the right along the x-axis, the line rises by two units on the y-axis. The slope of the parallel line through the point \( (-4, 2) \) is also 2. Parallel lines share the same slope, so this new line will rise in the same manner as the original line, maintaining that consistent steepness, no matter where it intersects the y-axis!

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