## How to Graph Lines by Using Slope–Intercept Form

Read,3 minutes

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:**

### Exercises for Graphing Lines Using Slope Intercept Form

**1) **Sketch the graph of the line: \(y \ = \ 3x \ + \ 2\)

**2) **Sketch the graph of the line: \(y \ = \ 2x \ + \ 1\)

**3) **Sketch the graph of the line: \(y \ = \ x \ + \ 5\)

**4) **Sketch the graph of the line: \(y \ = \ 3x \ - \ 2\)

**5) **Sketch the graph of the line: \(y \ = \ x \ - \ 2\)

**6) **Sketch the graph of the line: \(y \ = \ 4x \ + \ 1\)

**7) **Sketch the graph of the line: \(y \ = \ 2x \ - \ 3\)

**8) **Sketch the graph of the line: \(y \ = \ 3x \ - \ 4\)

**9) **Sketch the graph of the line: \(y \ = \ \frac{1}{2} \ x \ + \ 1\)

**10) **Sketch the graph of the line: \(y \ = \ 2x \ - \ 5\)

**1) **Sketch the graph of the line: \(y \ = \ 3x \ + \ 2\)

\(\color{red}{m \ = \ 3, \ b \ = \ 2 \ ⇒}\)

**2) **Sketch the graph of the line: \(y \ = \ 2x \ + \ 1\)

\(\color{red}{m \ = \ 2, \ b \ = \ 1 \ ⇒}\)

**3) **Sketch the graph of the line: \(y \ = \ x \ + \ 5\)

\(\color{red}{m \ = \ 1, \ b \ = \ 5 \ ⇒}\)

**4) **Sketch the graph of the line: \(y \ = \ 3x \ - \ 2\)

\(\color{red}{m \ = \ 3, \ b \ = \ -2 \ ⇒}\)

**5) **Sketch the graph of the line: \(y \ = \ x \ - \ 2\)

\(\color{red}{m \ = \ 1, \ b \ = \ -2 \ ⇒}\)

**6) **Sketch the graph of the line: \(y \ = \ 4x \ + \ 1\)

\(\color{red}{m \ = \ 4, \ b \ = \ 1 \ ⇒}\)

**7) **Sketch the graph of the line: \(y \ = \ 2x \ - \ 3\)

\(\color{red}{m \ = \ 2, \ b \ = \ -3 \ ⇒}\)

**8) **Sketch the graph of the line: \(y \ = \ 3x \ - \ 4\)

\(\color{red}{m \ = \ 3, \ b \ = \ -4 \ ⇒}\)

**9) **Sketch the graph of the line: \(y \ = \ \frac{1}{2} \ x \ + \ 1\)

\(\color{red}{m \ = \ \frac{1}{2} \ , \ b \ = \ 1 \ ⇒}\)

**10) **Sketch the graph of the line: \(y \ = \ 2x \ - \ 5\)

\(\color{red}{m \ = \ 2, \ b \ = \ -5 \ ⇒}\)