Lesson 10Meet Slope
Learning Goal
Let’s learn about the slope of a line.
Learning Targets
I can draw a line on a grid with a given slope.
I can find the slope of a line on a grid.
Lesson Terms
- similar
- slope
Warm Up: Equal Quotients
Problem 1
Write some numbers that are equal to
Activity 1: Similar Triangles on the Same Line
Problem 1
The figure shows three right triangles, each with its longest side on the same line.
Your teacher will assign you two triangles. Explain why the two triangles are similar.
Problem 2
Complete the table.
triangle | length of vertical side | length of horizontal side | (vertical side) |
---|---|---|---|
Activity 2: Multiple Lines with the Same Slope
Problem 1
Draw two lines with slope 3. What do you notice about the two lines?
Draw two lines with slope
. What do you notice about the two lines?
Print Version
Draw two lines with slope 3. What do you notice about the two lines?
Draw two lines with slope
. What do you notice about the two lines?
Are you ready for more?
Problem 1
As we learn more about lines, we will occasionally have to consider perfectly vertical lines as a special case and treat them differently. Think about applying what you have learned in the last couple of activities to the case of vertical lines. What is the same? What is different?
Activity 3: Different Slopes of Different Lines
Problem 1
Here are several lines. Match each line shown with a slope from this list:
, , , , ,
One of the given slopes does not have a line to match. Draw a line with this slope on the empty grid (f).
Lesson Summary
Here is a line drawn on a grid. There are also four right triangles drawn. Do you notice anything the triangles have in common?
These four triangles are all examples of slope triangles. One side of a slope triangle is on the line, one side is vertical, and another side is horizontal. The slope of the line is the quotient of the length of the vertical side and the length of the horizontal side of the slope triangle. This number is the same for all slope triangles for the same line because all slope triangles for the same line are similar.
In this example, the slope of the line is
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