Digits 5.3 (Day 1) Types of Slopes & Rise/Run

Slope

Slope is the measure of the steepness of a line! What is slope? Slope is the measure of the steepness of a line!

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.

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!

Quadrant II Quadrant I Quadrant III Quadrant IV Let’s review… y-axis Positive Quadrant II Quadrant I Positive Negative x-axis Negative Quadrant III Quadrant IV

How do you calculate slope? Slope is a ratio and represented by the variable m. One way to figure out slope is remember the ratio rise over run:

When you are given points on a line, you can calculate the slope by the following steps: 1. Write slope ratio. 2. Start at one point & find the vertical rise to the other point. 3. Start at the same point again and find the horizontal run. 4. Simplify

Steps to find the slope- Example 1 1. Write slope ratio. 2. Start at point A & find the vertical rise to point B. y 3. Find the horizontal run. • B x 4. Simplify • A

• • Example 2 Find the slope of the line. 1. Write slope ratio. 2. Start at either point. Find the vertical rise. y • 3. Find the horizontal run. • x

 NEVER change an improper fraction to a mix number. Why? When simplifying slope…. NEVER change an improper fraction to a mix number. Why? 

zero ooooover the denominator Example 3 Find the slope of the line. 1. Write slope ratio. y 2. Start at either point. Find the vertical rise. 3. Find the horizontal run. x • • 4. Simplify zero ooooover the denominator (zeroooooo slope)

zero unnnnder the numerator (unnnnndefined slope) Example 4 Find the slope of the line. 1. Write slope ratio. y 2. Start at either point. Find the vertical rise. • 3. Find the horizontal run. x • 4. Simplify zero unnnnder the numerator (unnnnndefined slope)

Student Companion Pg. 106 Part 1 (Got it 1 & 2)

Digits 5.3 (Day 2) Calculating Slope

Another way to calculate slope… m = run change in x rise change in y =

change in y m = change in x When you are given ordered pairs, you can calculate the slope by the following steps: 1. Stack the points m = run change in x rise change in y = change in y 2. Write the formula change in x 3. Substitute numbers for your variables 4. Solve & simplify

3. Substitute numbers for your variables Example 1 Find the slope of the line that passes through the points (2,4) and (-1,5). 1. Stack the points   2. Write the formula 3. Substitute numbers for your variables 4. Solve & simplify

Example 2 Find the slope of the line that passes through the points 1. Stack the points   2. Write the formula 3. Substitute numbers for your variables 4. Solve & simplify

Zero oooooover the line Example 3 Find the slope of the line that passes through the points 1. Stack the points   2. Write the formula 3. Substitute numbers for your variables Zero oooooover the line (zeroooooo slope) 4. Solve & simplify

Student Companion Part 2 & 3

PRACTICE. Plot the points and draw the line that passes through them PRACTICE. Plot the points and draw the line that passes through them. Without finding the slope, determine whether the slope is positive, negative, zero, or undefined. 3. (4,5) and (2,2) 4. (6,1) and (– 4,1) 5. (2,2) and (–1,4) 6. (3,6) and (3,–1) Find the slope by walking the line. y y 8. 7. • • x x • •

PRACTICE. Plot the points and draw the line that passes through them PRACTICE. Plot the points and draw the line that passes through them. Without finding the slope, determine whether the slope is positive, negative, zero, or undefined. 3. (4,5) and (2,2) 4. (6,1) and (– 4,1) 5. (2,2) and (–1,4) 6. (3,6) and (3,–1) Find the slope by walking the line. y y 8. 7. • • x x • •

Practice Problems Find the slope using the slope formula. (4,5) and (2,2) 2) (6,1) and (– 4,1) (2,2) and (–1,4) 4) (3,6) and (3,–1) 5. (2,-1) and (3,4) 6) (-3,-7) and (3,-7) undefined 5

Finding Slope from a table

Watch Video: https://www.youtube.com/watch?v=9lfN2ka-WNg

Now you try… Watch Video: https://www.youtube.com/watch?v=9lfN2ka-WNg

Challenging Questions

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Zero unnnnnder the line is unnnnndefined. Okay, so you use the slope formula and you generate the fraction . Zero unnnnnder the line is unnnnndefined. What is the answer? Undefined

Zero oooooover the line is You use the slope formula and generate a fraction like . What is the answer? Zero oooooover the line is zeroooooo.

Zero unnnnder the line is unnnnndefined. Example 3 Find the slope of the line that passes through the points   Zero unnnnder the line is unnnnndefined.