Day 21 – Slope

Slopes are commonly associated with mountains.

The slope we are studying is associated with the graph of a line.

Definitions of Slope The tilt or inclination of a line The ratio of vertical change to horizontal change. The change in y over the change in x Allow students time to copy May need to review that a ratio is a comparison of numbers

Tilt or Inclination Discuss positive and negative slope. Discuss when slope equals 0 and is undefined.

Vertical Change Horizontal Change This ratio is also known as 𝑹𝒊𝒔𝒆 𝑹𝒖𝒏

How many points do you need to draw a line? One Two Three Quiz students

Graph (3,2) and (-1,-1) Remember to click to make each part appear

Draw a line through the points. Line will appear automatically

Now that we have our line lets find its slope. Remember we are finding the following ratio: Vertical or Rise Horizontal Run

Vertical Change or the Rise 3 Discuss vertical change

Horizontal Change or the Run 4 3 Discuss horizontal change

Vertical Rise Horizontal Run 3 4 May need to remind students that a ratio is a comparison of two numbers

Find the slope of the following line.

The slope is… 1 2

Find the slope of the line.

The slope is…. -3 Discuss why the slope is negative and that –3/1 reduces to –3.

Find the slope of these lines. Have students practice.

The slope is… Black line = 3 Red Line = 1

Find the slope of these lines

The slope is… Orange line 0 Green Line Undefined

Let’s draw a line using slope. What else do you think you need besides the slope in order to draw a line? A point!

If you know the slope and one point on the line you can draw the line If you know the slope and one point on the line you can draw the line. Example: slope is 1/3 and the point (-2,-1)

Now you draw a line. Given: slope is 2/3 and the point is (1,0)

The graphs are…

Student Activity You will now receive a worksheet. You are to find the slope of a line and draw a line given the slope and a point. Turn the worksheet in when completed.

Work Time

1/2 -2/3

1/2 -3

-1 1

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Given a point and a slope draw the line.

Change in y over the change in x The formula for finding the slope of a line.

Class Activity Click on the following link for slope practice. If link does not work go to www.exploremath.com/activities/Activity_page.cfm Or go go to www.exploremath.com, click on lines/linear equations, click on slope calculation. Demonstrate web activity one time. Then have students come up and pick different numbers and have class find the slope together. If no link do all examples on the board. Students can still pick points.

Closing Activity You will receive a second worksheet. Given 2 points, find the slope using the slope formula. You will turn in the worksheet. More than likely this worksheet will be homework.