Big Ideas Math Integrated I, 2016
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Big Ideas Math Integrated I, 2016 View details
3. Writing Equations of Parallel and Perpendicular Lines
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Exercise 31 Page 182

Calculate the slopes of the lines and find their product.

No, see solution.

Practice makes perfect

If our friend is correct and the path of the puck forms a right angle, then the two lines that form the path are perpendicular. Slopes of perpendicular lines are negative reciprocals, meaning their product is - 1. To check this, we first have to find the slopes.

First Line

From the graph we can tell that the line passes through the points (- 4,0) and (0,8). Let's substitute these points into the Slope Formula.

m_1=y_2-y_1/x_2-x_1
m_1=8- 0/0-( - 4)
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Simplify right-hand side
m_1=8-0/0+4
m_1=8/4
m_1=2
The slope of the first line is 2.

Second Line

The second line passes through the points (0,8) and (- 4,16). Again, we will substitute these two points into the Slope Formula to find the slope of the second line that makes the path.

m_2=y_2-y_1/x_2-x_1
m_2=16- 8/- 4- 0
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Simplify right-hand side
m_2=8/- 4
m_2=- 8/4
m_2=- 2

The slope of the second line is - 2.

Product

Let's multiply our slopes and check if the product equals - 1.

m_1* m_2 ? =- 1
2 ( - 2) ? =- 1
- 2* 2 ? =- 1
- 4 ≠ - 1 *

Since the product of the slopes is not - 1, the lines are not perpendicular. Consequently, our friend was incorrect.