Question

Consider the following graphs of linear equations. Decide which line has a positive slope, and which has a negative slope. Then calculate each line’s exact slope.

(Lesson 3-10)

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Line L
Line M

Answer 1

Line L has a positive slope, while Line M has a negative slope.

To determine the slope of a line, we can use the formula:

slope = (change in y-coordinates) / (change in x-coordinates)

Looking at Line L, we can see that as x increases, y also increases. This indicates a positive slope. To calculate the exact slope, we can choose two points on the line and find the change in y-coordinates divided by the change in x-coordinates.

Let's choose the points (1, 2) and (3, 4) on Line L.

change in y-coordinates = 4 - 2 = 2

change in x-coordinates = 3 - 1 = 2

slope = (change in y-coordinates) / (change in x-coordinates) = 2 / 2 = 1

Therefore, Line L has a positive slope of 1.

Now, let's look at Line M. As x increases, y decreases. This indicates a negative slope. Similarly, we can choose two points on Line M to calculate the exact slope.

Let's choose the points (1, 4) and (3, 2) on Line M.

change in y-coordinates = 2 - 4 = -2

change in x-coordinates = 3 - 1 = 2

slope = (change in y-coordinates) / (change in x-coordinates) = -2 / 2 = -1

Therefore, Line M has a negative slope of -1.