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Chapter 0: Problem 27

Finding the Slope and \(y\) -lntercept In Exercises \(25-30\) , find the slope and the \(y\) -intercept (if possible) of the line. $$ x+5 y=20 $$

Short Answer

Expert verified
The slope of the line is -1/5 and the y-intercept is 4.

Step by step solution

01

Rewrite the Equation

The first step is to rewrite the given equation \(x + 5y = 20\) in terms of \(y\). Start with subtracting \(x\) from both sides of the equation to isolate \(5y\). This results in the equation \(5y = 20 - x\).
02

Solve for y

To obtain the equation in the form \(y=mx+b\), the equation has to be rewritten in terms of \(y\). Thus, divide all terms by 5, which gives us the equation \(y = -\frac{1}{5}x + 4\).
03

Identify the Slope and y-Intercept

In the rewritten equation \(y =-(1/5)x + 4\), a comparison with the general slope-intercept form of a line \(y = mx + b\) yields that the slope (m) is -1/5 and the y-intercept (b) is 4.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Slope-Intercept Form
The slope-intercept form is one of the most common ways to represent a linear equation. It's written as \(y = mx + b\), where \(m\) represents the slope of the line, and \(b\) represents the y-intercept.

Understanding the slope-intercept form is crucial for graphing linear equations, as it readily gives you the steepness of the line (\

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Most popular questions from this chapter

Even and Odd Functions and Zeros of Functions In Exercises \(79-82\) , determine whether the function is even, odd, or neither. Then find the zeros of the function. Use a graphing utility to verify your result. $$ f(x)=x^{2}\left(4-x^{2}\right) $$

True or False? In Exercises \(93-96,\) determine whether the statement is true or false. If it is false, explain why or give an example that shows it is false. The lines represented by \(a x+b y=c_{1}\) and \(b x-a y=c_{2}\) are perpendicular. Assume \(a \neq 0\) and \(b \neq 0\)

Domain Find the value of \(c\) such that the domain of \(f(x)=\sqrt{c-x^{2}}\) is \([-5,5]\)

Deciding Whether an Equation Is a Function In Exercises \(47-50\) , determine whether \(y\) is a function of \(x .\) $$ x^{2}+y=16 $$

Finding the Domain and Range of a Function In Exercises \(11-22,\) find the domain and range of the function. $$ f(x)=x^{3} $$
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