# How to Graph Lines by Using Slope–Intercept Form

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

• $$\color{blue}{y = \frac{1}{ 2} x – 4}$$
• $$\color{blue}{y = 2x}$$

• $$\color{blue}{y = \frac{1}{ 2} x – 4}$$
• $$\color{blue}{y = 2x}$$

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