Warm-Up

Finding The Slope of a Line Unit 6 Day 1 Finding The Slope of a Line

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.

Types of Slope: Zero Positive Negative No Slope Or Undefined Discuss positive and negative slope. Discuss when slope equals 0 and is undefined. Negative No Slope Or Undefined

Vertical Change Horizontal Change SLOPE 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

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

Draw a line through the points. Line will appear automatically

Ex 2: 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

Ex 3: Find the slope of the following line.

The slope is… 1 2

Ex 4: Find the slope of the line.

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

Ex 5: Find the slope of these lines. Have students practice.

The slope is… Black line 3 Red Line 1 Blue Line -1/2

Ex 6: 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!

7. 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. 8. Given: slope is 2/3 and the point is (1,0)

The graphs are…

Slope Formula We can also find the slope of a line if we are given two points. We use the Slope Formula:

Ex 1: Find the slope of a line given the points (3,-4) and (-7,1).

Find the slope of the line that passes between the points: Ex 2:(-2,6) and (-3,2) Ex 3:(4,1) and (4,-8) Ex 4:(0,-5) and (-11,-5)