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Graphs of Linear Equations

7.10.1 Graphs of Linear Equations

7.10.1 • Graphs of Linear Equations

Warm Up

Here is a graph of the equation y=8−2xy=8−2x.

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.
1.

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

Compare your answer:

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

2.

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)(0,8) and (1,6)(1,6). When xx increases by 1, yy decreases by 2.

3.

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

The xx-intercept is (4,0)(4,0). The 4 is the solution of 8−2x=08−2x=0.