Obj: to find the slope of a line 5.4 Slope Formula

Warm-Up Find the intercepts 1. x + 2y = x + 5y = –15 x-intercept: –5; y-intercept: –3 x-intercept: 8; y-intercept: 4

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Slope Formula

Example 1: Finding Slope by Using the Slope Formula Find the slope of the line that contains (2, 5) and (8, 1). Use the slope formula. Substitute (2, 5) for (x 1, y 1 ) and (8, 1) for (x 2, y 2 ). Simplify. The slope of the line that contains (2, 5) and (8, 1) is.

Find the slope of the line that contains (–2, –2) and (7, –2). Example 2 Use the slope formula. Substitute (–2, – 2) for (x 1, y 1 ) and (7, –2) for (x 2, y 2 ). Simplify. The slope of the line that contains (–2, –2) and (7, –2) is 0. = 0

Sometimes you are not given two points to use in the formula. You might have to choose two points from a graph or a table.

Example 3 The graph shows a linear relationship. Find the slope. Let (0, 2) be (x 1, y 1 ) and (–2, –2) be (x 2, y 2 ). Simplify. Use the slope formula. Substitute (0, 2) for (x 1, y 1 ) and (–2, –2) for (x 2, y 2 ).

Example 4 The table shows a linear relationship. Find the slope. Step 1 Choose any two points from the table. Let (0, 1) be (x 1, y 1 ) and (2, 5) be (x 2, y 2 ). Step 2 Use the slope formula. Use the slope formula. Simplify. Substitute (0, 1) for (x 1, y 1 ) and (2, 5) for (x 2, y 2 ).

Example 5: Application The graph shows the average electricity costs (in dollars) for operating a refrigerator for several months. Find the slope of the line. Then tell what the slope represents. Step 1 Use the slope formula.

Example 5 Continued Step 2 Tell what the slope represents. In this situation y represents the cost of electricity and x represents time. So slope represents in units of. A slope of 6 mean the cost of running the refrigerator is a rate of 6 dollars per month.

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