Holt McDougal Algebra Rate of Change and Slope 4-3 Rate of Change and Slope Holt Algebra 1 Lesson Quiz Lesson Quiz Lesson Presentation Lesson Presentation Warm Up Warm Up Holt McDougal Algebra 1

4-3 Rate of Change and Slope A rate of change is a ratio that compares the amount of change in a dependent variable to the amount of change in an independent variable.

Holt McDougal Algebra Rate of Change and Slope

Holt McDougal Algebra Rate of Change and Slope As shown in the previous examples, slope can be positive, negative, zero or undefined. You can tell which of these is the case by looking at a graph of a line–you do not need to calculate the slope.

Holt McDougal Algebra Rate of Change and Slope Example 3: Finding Slope Find the slope of the line. Begin at one point and count vertically to fine the rise. Then count horizontally to the second point to find the run. It does not matter which point you start with. The slope is the same. (3, 2) (–6, 5) Rise 3 Run –9 Rise –3 Run 9

Holt McDougal Algebra Rate of Change and Slope Check It Out! Example 3 Find the slope of the line that contains (0, –3) and (5, –5). Begin at one point and count vertically to find rise. Then count horizontally to the second point to find the run. It does not matter which point you start with. The slope is the same. Rise 2 Run –5 Rise –2 Run 5

Holt McDougal Algebra Rate of Change and Slope

Holt McDougal Algebra Rate of Change and Slope 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.

Holt McDougal Algebra Rate of Change and Slope Example 2A: Finding Slope from Graphs and Tables 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 ).

Holt McDougal Algebra Rate of Change and Slope Find the slope of the line that contains (5, –7) and (6, –4). Check It Out! Example 1b 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 McDougal Algebra Rate of Change and Slope Check It Out! Example 2d 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. Use the slope formula. Simplify Substitute (0, 0) for (x 1, y 1 ) and (–2, 3) for (x 2, y 2 ).

Holt McDougal Algebra Rate of Change and Slope Example 4: Finding Slope from an Equation Find the slope of the line described by 4x – 2y = 16. Step 1 Find the x-intercept.Step 2 Find the y-intercept. 4x – 2y = 16 4x = 16 x = 4 Step 3 The line contains (4, 0) and (0, –8). Use the slope formula. 4x – 2y = 16 –2y = 16 y = –8 4x – 2(0) = 16 Let y = 0. 4(0) – 2y = 16 Let x = 0.