Chapter 1: Q. 12 (page 40)

In problems $11 - 14, (a)$ find the slope of the line and $(b)$ intercept the slope.

Short Answer

Expert verified

(a) The slope of the line is $m = - \frac{1}{2}$ .

(b) The line makes an angle $π - \tan^{- 1} (\frac{1}{2})$ with positive $x -$ axis.

Step by step solution

Step 1. Given information.

We have the graph given below:

Part (a). Step 1. Find slope.

Two are are given in given graph:

$(- 2, 1)$ and $(0, 0)$

Slope between two points: $Slope = \frac{y_{2} - y_{1}}{x_{2} - x_{1}}$

$(x_{1}, y_{1}) = (- 2, 1), (x_{2}, y_{2}) = (0, 0) m = \frac{0 - 1}{0 - (- 2)} m = - \frac{1}{2}$

Part (b). Step 1. Intercept the slope.

Slope of the line is given by:

$m = \tan θ - \frac{1}{2} = \tan θ θ = \tan^{- 1} (- \frac{1}{2}) θ = π - \tan^{- 1} (\frac{1}{2})$

Therefore, the line makes an angle $π - \tan^{- 1} (\frac{1}{2})$ with the positive $x -$ axis.

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In problems $11 - 14, (a)$ find the slope of the line and $(b)$ intercept the slope.

Short Answer

Step by step solution

Step 1. Given information.

Part (a). Step 1. Find slope.

Part (b). Step 1. Intercept the slope.

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In problems 11-14,(a)find the slope of the line and bintercept the slope.

Short Answer

Step by step solution

Step 1. Given information.

Part (a). Step 1. Find slope.

Part (b). Step 1. Intercept the slope.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Discrete Mathematics

Theoretical and Mathematical Physics

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Probability and Statistics

Geometry

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Study anywhere. Anytime. Across all devices.

In problems $11 - 14, (a)$ find the slope of the line and $(b)$ intercept the slope.