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Chapter 4: Problem 9

Explain how to find an equation of a line when you are given the slope and \(y\) -intercept of the line.

Short Answer

Expert verified
To find an equation of a line with a given slope 'm' and y-intercept 'b', use the slope-intercept form of a linear equation: \( y = mx + b \). Substitute the given values for 'm' and 'b' into the equation and simplify, if needed. The final linear equation will be in the form \( y = mx + b \) with the given slope and y-intercept values.

Step by step solution

01

Identify the given slope and y-intercept

We are given the slope 'm' and y-intercept 'b' of the line.
02

Write down the slope-intercept form of a linear equation

The slope-intercept form of a linear equation is given by: \( y = mx + b \)
03

Plug the given slope and y-intercept into the slope-intercept form

Replace 'm' with the given slope, and 'b' with the given y-intercept in the equation: \( y = mx + b \)
04

Simplify the equation (if needed)

If there are any like terms or any terms that can be simplified, do so.
05

Write down the final linear equation

Now, we have found the equation of the line with the given slope and y-intercept. The final linear equation should be in the form: \( y = mx + b \), with the given slope and y-intercept values substituted in.

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