7.10.1 Graphs of Linear Equations

Algebra 17.10.1 Graphs of Linear Equations

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Warm Up

Here is a graph of the equation $y = 8 - 2 x$ .

The graph of a line on a coordinate grid. The x-axis has a scale of 1 and extends from negative 2 to 5 while the y-axis has a scale of 2 and extends from negative 2 to 12.

Where do you see the 8 from the equation in the graph?

Compare your answer:

The 8 in $y = 8 - 2 x$ means the graph intersects the $y$ -axis at 8. The $y$ -intercept is (0,8).

Where do you see the –2 from the equation in the graph?

Compare your answer:

The –2 is the slope of the line. You can see it, for example, by looking at $(0, 8)$ and $(1, 6)$ . When $x$ increases by 1, $y$ decreases by 2.

What is the value of $x$ for the $x$ -intercept of the graph? How does this relate to the equation?

The $x$ -intercept is $(4, 0)$ . The 4 is the solution of $8 - 2 x = 0$ .

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- Authors: Lynn Marecek, MaryAnne Anthony-Smith, Andrea Honeycutt Mathis, Jay Abramson, Sharon North, Amy Baldwin, Alyssa Howell
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- Book title: Algebra 1
- Publication date: Jun 4, 2025
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