Objective Find slope by using the slope formula..

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Presentation transcript:

Objective Find slope by using the slope formula.

Example 1: Find the slope of the line that contains (2, 5) and (8, 1). Use the slope formula. Substitute (2, 5) for (x1, y1) and (8, 1) for (x2, y2). Simplify. The slope of the line that contains (2, 5) and (8, 1) is .

Example 2 Find the slope of the line that contains (–2, –2) and (7, –2). Use the slope formula. Substitute (–2, –2) for (x1, y1) and (7, –2) for (x2, y2). Simplify. = 0 The slope of the line that contains (–2, –2) and (7, –2) is 0.

Example 3 Find the slope of the line that contains (5, –7) and (6, –4). Use the slope formula. Substitute (5, –7) for (x1, y1) and (6, –4) for (x2, y2). Simplify. = 3 The slope of the line that contains (5, –7) and (6, –4) is 3.

Sometimes you are not given two points to use in the formula 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 4: Finding Slope from Graphs The graph shows a linear relationship. Find the slope. Let (0, 2) be (x1, y1) and (–2, –2) be (x2, y2). Use the slope formula. Substitute (0, 2) for (x1, y1) and (–2, –2) for (x2, y2). Simplify.

Example 5: Finding Slope from Tables The table shows a linear relationship. Find the slope. Step 1 Choose any two points from the table. Let (0, 1) be (x1, y1) and (–2, 5) be (x2, y2). Step 2 Use the slope formula. Use the slope formula. Substitute (0, 1) for and (–2, 5) for . Simplify. The slope equals −2

The table shows a linear relationship. Find the slope. Example 6 The table shows a linear relationship. Find the slope. Step 1 Choose any two points from the table. Let (0, 0) be (x1, y1) and (–2, 3) be (x2, y2). Step 2 Use the slope formula. Use the slope formula. Substitute (0, 0) for (x1, y1) and (–2, 3) for (x2, y2). Simplify

Remember that slope is a rate of change Remember that slope is a rate of change. In real-world problems, finding the slope can give you information about how a quantity is changing.

Example 7 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 7 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.