Objective Find slope by using the slope formula

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 (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.

Example 2 Find the slope of the line that contains (– 2, – 2) and (7, – 2). Use the slope formula. Substitute (– 2, – 2) for (x 1, y 1) and (7, – 2) for (x 2, y 2). 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 (x 1, y 1) and (6, – 4) for (x 2, y 2). 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. 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 (x 1, y 1) and (– 2, – 2) be (x 2, y 2). Use the slope formula. Substitute (0, 2) for (x 1, y 1) and (– 2, – 2) for (x 2, y 2). 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 (x 1, y 1) and (– 2, 5) be (x 2, y 2). Step 2 Use the slope formula. Substitute (0, 1) for and (– 2, 5) for. Simplify. The slope equals − 2

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

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.