Chapter 8: Q31. (page 410)

Write the equation in function form. Then graph the equation.
$2 x + 3 y = 12$

Short Answer

Expert verified

The function form of our given equation would be $y = - \frac{2}{3} x + 4$ .

Step by step solution

Step 1. Given Information.

An equation: $2 x + 3 y = 12$

Step 2. Calculation.

To write the given equation in function form, we need to convert our equation in slope-intercept form $(y = m x + b)$ as:

$\begin{matrix} 2 x + 3 y = 12 (Givenequation) \\ 2 x - 2 x + 3 y = 12 - 2 x (Subtracting2 x frombothsides) \\ 3 y = - 2 x + 12 \\ \frac{3 y}{3} = \frac{- 2 x}{3} + \frac{12}{3} (Dividingbothsidesby 3) \\ y = - \frac{2}{3} x + 4 \end{matrix}$

Therefore, the function form of our given equation would be $y = - \frac{2}{3} x + 4$ .

We can see that the slope of our given equation is $- \frac{2}{3}$ and the y-intercept is $(0, 4)$ .

Upon graphing our given equation, we will get our required graph as shown below:

Step 3. Conclusion.

The function form of our given equation would be $y = - \frac{2}{3} x + 4$ .

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.

Write the equation in function form. Then graph the equation.
$2 x + 3 y = 12$

Short Answer

Step by step solution

Step 1. Given Information.

Step 2. Calculation.

Step 3. Conclusion.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Mechanics Maths

Decision Maths

Discrete Mathematics

Pure Maths

Probability and Statistics

Logic and Functions

Study anywhere. Anytime. Across all devices.

Write the equation in function form. Then graph the equation.2x+3y=12

Short Answer

Step by step solution

Step 1. Given Information.

Step 2. Calculation.

Step 3. Conclusion.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Mechanics Maths

Decision Maths

Discrete Mathematics

Pure Maths

Probability and Statistics

Logic and Functions

Study anywhere. Anytime. Across all devices.

Write the equation in function form. Then graph the equation.
$2 x + 3 y = 12$