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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