How to Graph Lines by Using Slope–Intercept Form

How to Graph Lines by Using Slope–Intercept Form?

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There are several ways to graph linear equations. Utilizing slope-intercept form is one of the fastest and simplest methods of graphing a linear equation. Prior to starting, we have to explain some of the vocabulary. We will discuss \(x\) and \(y\) intercepts.
An \(x\) intercept is the point where the line crosses the \(x\)-axis. The \(y\) intercept is the point where the line crosses the \(y\)-axis.
We're merely going to concentrate on the \(y\) intercept for this lesson, however, you will have to know about the \(x\) intercept for later.

Look over at intercepts.

Slope intercept form is utilized whenever the linear equation is written as: \(y \ = \ mx \ + \ b\)
\(x\) and \(y\) are the variables. \(m\) is going to be a numeral, which is your slope. \(b\) is also going to be a numeral and that is the \(y\)-intercept.

In this form only (whenever the equation is written as \(y \ = \ ...\) ) the coefficient of \(x\) is the slope and the constant is the \(y\) intercept.
Whenever an equation is written in this form, you can view the equation and have sufficient info for graphing it.
For instance, imagine you have the equation \(y \ = \ 3x \ + \ 1\) and are told to graph it.
Straight from the equation, you can see the \(y\)-intercept is \(1\). Plus you know the slope is \(3\).
\(slop \ = \ \frac{∆y}{∆x} \ = \ \frac{3}{1} \ = \ 3\)
Therefore, for every one unit you go to the right, so we have to go up three units:

A first quadrant coordinate plane. The \(x\) and \(y\)-axes each scale by one. A graph of the line goes through the points \((0,1)\) and \((1,4)\) which have been plotted. There’s a horizontal segment from \((0,1)\) to \((1,1)\). There’s a vertical line from \((1,1)\) to \((1,4)\).

Here’s the final graph:

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