Unit 2, Lesson 10
Meet Slope
Grade 8
10.1
Warm-up
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Choose a scale factor and draw a dilation of triangle using point as the center of dilation. What scale factor did you use?
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Use a piece of tracing paper to trace point and your dilated figure. Compare your dilation with your group. What do you notice?
10.2
Activity
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The grid shows three right triangles, each with its longest side on the same line. Your teacher will assign you two of the triangles. Explain why the two triangles are similar.
- Complete the table.
triangle length of
vertical sidelength of
horizontal side(vertical side) (horizontal side) 3 4 or 0.75 - What do you notice about the last column in the table? Why do you think this is true?
10.3
Activity
- Draw two lines with a slope of 3. What do you notice about the two lines?
- Draw two lines with a slope of . What do you notice about the two lines?
Student Lesson Summary
Here is a line drawn on a grid. There are also four right triangles drawn.
<p>Four right triangles each with hypotenuse on the same line. First horizontal side 6, vertical side 4. Second horizontal side 3, vertical side 2. Third horizontal side 1, vertical side fraction 2 over 3. Fourth horizontal side 6, vertical side 4.</p>
These four triangles are all examples of slope triangles. The longest 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 vertical length and the horizontal length 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 . Here is how the slope is calculated using the slope triangles:
- Points and give .
- Points and give .
- Points and give .
- Points and give .
Slope is a number that describes how steep a line is. To find the slope, divide the vertical change by the horizontal change for any 2 points on the line.
The slope of this line is 2 divided by 3, or .