Learn how to graph lines using the equation of the line in slope–intercept form.

## Related Topics

- How to Find Midpoint
- How to Find Slope
- How to Graph Linear Inequalities
- How to Write Linear Equations
- How to Graph Lines by Using Standard Form

## Step by step guide to graphing lines using slope–intercept form

- Slope–intercept form of a line: given the slope \(m\) and the \(y\)–intercept (the intersection of the line and \(y\)-axis) \(b\) , then the equation of the line is:

\(y=mx+b\)

### Graphing Lines Using Slope–Intercept Form – Example 1:

Sketch the graph of \(y=6x-1\)

**Solution:**

To graph this line, we need to find two points. When \(x\) is zero the value of \(y\) is \(-1\). And when \(y\) is zero the value of \(x\) is \(\frac{1}{6}\).

\(x=0→y=6(0)-1= \ – \ 1, y=0→0=6x-1→x=\frac{1}{6}\)

Now, we have two points: \((0,-1)\) and \((\frac{1}{6},0)\). Find the points and graph the line. Remember that the slope of the line is \(6\).

### Graphing Lines Using Slope–Intercept Form – Example 2:

Sketch the graph of \(y=8x-3\).

**Solution:**

To graph this line, we need to find two points. When \(x\) is zero the value of \(y\) is \(-3\). And when y is zero the value of \(x\) is \(\frac{3}{8}\). \(x=0→y=8(0)-3=-3, y=0→0=8x-3→x=\frac{3}{8}\)

Now, we have two points: \((0,-3)\) and \((\frac{3}{8},0)\). Find the points and graph the line. Remember that the slope of the line is \(8\).

## Exercises for Graphing Lines Using Slope–Intercept Form

### Sketch the graph of each line.

- \(\color{blue}{y = \frac{1}{ 2} x – 4}\)

- \(\color{blue}{y = 2x}\)

### Download Graphing Lines Using Line Equation Worksheet

- \(\color{blue}{y = \frac{1}{ 2} x – 4}\)

- \(\color{blue}{y = 2x}\)