Chapter 1: Q. 14 (page 40)

In problems $11 - 14, (a)$ find the slope of the line and role="math" localid="1645942833999" $(b)$ intercept the slope.

Short Answer

Expert verified

(a) The slope of the line is $m = - \frac{1}{3}$ .

(b) The line makes an angle $π - \tan^{- 1} (- \frac{1}{3})$ with the 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:

$(- 1, 1), (2, 2)$

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

$(x_{1}, y_{1}) = (1, 1), (x_{2}, y_{2}) = (- 2, 2)$

$m = \frac{2 - 1}{- 2 - 1} m = - \frac{1}{3}$

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

Slope of the line is given by:

$m = \tan θ - \frac{1}{3} = \tan θ θ = \tan^{- 1} (- \frac{1}{3}) θ = π - \tan^{- 1} (\frac{1}{3})$

Therefore, the line makes an angle $π - \tan^{- 1} (\frac{1}{3})$ with the positive $x -$ axis.

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In problems $11 - 14, (a)$ find the slope of the line and role="math" localid="1645942833999" $(b)$ 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 role="math" localid="1645942833999" (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.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Theoretical and Mathematical Physics

Applied Mathematics

Decision Maths

Mechanics Maths

Geometry

Statistics

Study anywhere. Anytime. Across all devices.

In problems $11 - 14, (a)$ find the slope of the line and role="math" localid="1645942833999" $(b)$ intercept the slope.