Chapter 3: Q. 458 (page 357)

In the following exercises, find the equation of the line shown in each graph. Write the equation in slope-intercept form.

Short Answer

Expert verified

The slope-intercept form of the equation of the line in the shown graph is $y = 2 x + 1$ .

Step by step solution

Step 1. Given information

The provided graph of a line equation is:

Step 2. Evaluate/formulas

From the graph, take two points that lie on the line are say $(1, 3), (0, 1) .$

The slope between two points $(x_{1}, y_{1}), (x_{2}, y_{2})$ is $m = \frac{y_{2} - y_{1}}{x_{2} - x_{1}}$ .

The point-slope from of the line equation that passes through the point $(x_{1}, y_{1})$ with slope $m$ isrole="math" localid="1646132732448" $y - y_{1} = m (x - x_{1})$ .

Step 3. Find the equation of the line.

Here, $(x_{1}, y_{1}) = (0, 1), (x_{2}, y_{2}) = (1, 3) .$

Find the slope.

$m = \frac{3 - 1}{1 - 0} m = 2$

Substitute $m = 2, x_{1} = 0, y_{1} = 1$ in $y - y_{1} = m (x - x_{1})$ .

$\begin{array}{rcl} y - 1 & = & 2 (x - 0) \\ y - 1 & = & 2 x \\ y & = & 2 x + 1 \end{array}$

The line equation is $\begin{array}{rcl} y & = & 2 x + 1 \end{array}$ .

Unlock Step-by-Step Solutions & Ace Your Exams!

Full Textbook Solutions
Get detailed explanations and key concepts
Unlimited Al creation
Al flashcards, explanations, exams and more...
Ads-free access
To over 500 millions flashcards
Money-back guarantee
We refund you if you fail your exam.

Start your free trial

Over 30 million students worldwide already upgrade their learning with Vaia!

Recommended explanations on Math Textbooks

View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

In the following exercises, find the equation of the line shown in each graph. Write the equation in slope-intercept form.

Short Answer

Step by step solution

Step 1. Given information

Step 2. Evaluate/formulas

Step 3. Find the equation of the line.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Theoretical and Mathematical Physics

Calculus

Mechanics Maths

Discrete Mathematics

Logic and Functions

Probability and Statistics

Study anywhere. Anytime. Across all devices.