4-1A Rate of Change and the Slope of a Line Using a Graph

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Presentation transcript:

4-1A Rate of Change and the Slope of a Line Using a Graph Algebra 1 Glencoe McGraw-Hill Linda Stamper

Rate of change is a ratio that describes, on average, how much one quantity changes with respect to a change in another quantity. If x is the independent variable and y is the dependent variable, then x y 1 6 2 12 3 18 4 24 +1 +6 +6 +1 +6 +1 The rate of change is 6.

Example 1 Use the table to find the rate of change. x y 2 6 4 12 18 8 24 +2 +6 +6 +2 +6 +2 The rate of change is 3.

You have been graphing linear equations which graph as a line. In this lesson you will learn about slope. Slope is the steepness of a line.

You have been graphing linear equations which graph as a line. In this lesson you will learn about slope. Slope is the steepness of a line.

You have been graphing linear equations which graph as a line. In this lesson you will learn about slope. Slope is the steepness of a line. Slope is a ratio of rise to run.

Find the slope of a hill that has a vertical rise of 40 feet and a horizontal run of 200 feet. Let m represent slope. Write word ratio. Substitute. Simplify – write in lowest terms.

Example 2 Find the slope of a wheelchair ramp that has a vertical rise of 2 feet and a horizontal run of 24 feet. Let m represent slope. Example 3 Find the slope of a ski trail that has a vertical rise of -3 feet and a horizontal run of 4 feet. Let m represent slope.

Types of Slope Imagine that you are walking to the right on a line. A positive slope means that you are walking uphill.

Types of Slope Imagine that you are walking to the right on a line. A negative slope means that you are walking downhill.

Types of Slope Imagine that you are walking to the right on a line. Zero slope means that you are walking on level ground. Do not identify this as “no slope”.

Types of Slope Undefined slope is a vertical line. You can not walk up a vertical line. It is not possible. You would fall! ouch! Do not identify this as “no slope”.

Types of Slope are words! positive negative zero undefined

This means to calculate the slope - to find the steepness of the line! Find the Slope by Walking the Line This means to calculate the slope - to find the steepness of the line!

• • Find the Slope by Walking the Line When you find the slope by walking the line, moving upward on the graph is positive. y Moving left on the graph is negative. • x Moving downward on the graph is negative. • Moving right on the graph is positive.

• • Find the slope of the line. Write slope ratio. Write slope ratio. MANDATORY STEP Start at either point. Find the vertical rise. Up is positive and down is negative. y Find the horizontal run. Going right is positive and going left is negative. • x • Simplify.

• • • • • Find the slope of the line. Write slope ratio. Start at either point. Find the vertical rise. Up is positive and down is negative. y • • Find the horizontal run. Going right is positive and going left is negative. • x • • Simplify. Slope is the rate of change. It will change -2 all along the line.

• • Example 4A Find the slope of the line. 1. Write slope ratio. y 2. Start at either point. Find the vertical rise. Up is positive and down is negative. • • x 3. Find the horizontal run. Going right is positive and going left is negative. It does not matter at which point you begin the walk!

• • Example 4B Find the slope of the line. 1. Write slope ratio. y 2. Start at either point. Find the vertical rise. Up is positive and down is negative. • • x 3. Find the horizontal run. Going right is positive and going left is negative. It does not matter at which point you begin the walk!

zero ooooover the fraction line is Example 5 Find the slope of the line. y 1. Write slope ratio. 2. Start at either point. Find the vertical rise. Up is positive and down is negative. x • • 3. Find the horizontal run. Going right is positive and going left is negative. zero ooooover the fraction line is (zeroooooo) 4. Simplify

zero unnnnder the fraction line is unnnnndefined Example 6 Find the slope of the line. y 1. Write slope ratio. 2. Start at either point. Find the vertical rise. Up is positive and down is negative. • x • 3. Find the horizontal run. Going right is positive and going left is negative. zero unnnnder the fraction line is unnnnndefined 4. Simplify

Writing the slope ratio is a mandatory step! PRACTICE. Plot the points and draw the line that passes through them. Then find the slope using the slope ratio. 1. (2,4) and (2,-4) 3. (3,6) and (3,–1) 5. (6,1) and (–4,1) 2. (4,5) and (2,2) 4. (-2,-3) and (3,-3) 6. (2,2) and (–1,4) Find the slope by walking the line. Writing the slope ratio is a mandatory step! y y 8. 7. • • x x • •

• • • • 1. (2,4) and (2,-4) 4. (-2,-3) and (3,-3) PRACTICE. Answers 1. (2,4) and (2,-4) 4. (-2,-3) and (3,-3) 2. (4,5) and (2,2) 5. (6,1) and (–4,1) 3. (3,6) and (3,–1) 6. (2,2) and (–1,4) y y 8. 7. • • x x • •

Homework 4-A2 SKILLS PRACTICE Wkbk. Page 24 #1–19 #4 – 19 Plot the points and draw the line that passes through them. Then find the slope using the slope ratio. Skip #12.