Holt Algebra The Slope Formula Warm Up Add or subtract (–6) 2. – –7 – – (–1) Find the x- and y-intercepts. 5. x + 2y = x + 5y = –15 x-intercept: –5; y-intercept: –3 x-intercept: 8; y-intercept: 4 –2 2 3 –14

Holt Algebra The Slope Formula Find slope by using the slope formula. Objective

Holt Algebra The Slope Formula In Lesson 5-3, slope was described as the constant rate of change of a line. You saw how to find the slope of a line by using its graph. There is also a formula you can use to find the slope of a line, which is usually represented by the letter m. To use this formula, you need the coordinates of two different points on the line.

Holt Algebra The Slope Formula

Holt Algebra The Slope Formula Directions: Find the slope, given two points (use the formula)

Holt Algebra 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.

Holt Algebra The Slope Formula 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

Holt Algebra The Slope Formula Find the slope of the line that contains (5, –7) and (6, –4). Example 3 Use the slope formula. Substitute (5, –7) for (x 1, y 1 ) and (6, –4) for (x 2, y 2 ). Simplify. The slope of the line that contains (5, –7) and (6, –4) is 3. = 3

Holt Algebra The Slope Formula Find the slope of the line that contains and Example 4 Use the slope formula. Substitute for (x 1, y 1 ) and for (x 2, y 2 ) and simplify. The slope of the line that contains and is 2.

Holt Algebra The Slope 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. Directions: Find two points on the graph or table and determine the slope using the formula.

Holt Algebra The Slope Formula Example 5 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 ).

Holt Algebra The Slope Formula Example 6 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. The slope equals −2 Use the slope formula. Substitute (0, 1) for and (–2, 5) for. Simplify.

Holt Algebra The Slope Formula Example 7 Simplify. Use the slope formula. Let (–2, 4) be (x 1, y 1 ) and (0, –2) be (x 2, y 2 ). Substitute (–2, 4) for (x 1, y 1 ) and (0, –2) for (x 2, y 2 ).

Holt Algebra The Slope Formula Example 8 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. Use the slope formula. Simplify Substitute (0, 0) for (x 1, y 1 ) and (–2, 3) for (x 2, y 2 ).

Holt Algebra The Slope Formula 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.

Holt Algebra The Slope Formula Example 9 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.

Holt Algebra The Slope Formula Example 9 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.

Holt Algebra The Slope Formula Lesson Summary 1. Find the slope of the line that contains (5, 3) and (–1, 4). 2. Find the slope of the line. Then tell what the slope represents. 50; speed of bus is 50 mi/h