How to Graph Lines by Using Slope–Intercept Form? (+FREE Worksheet!)

Watch this practice video for additional examples and reinforcement:

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 For education statistics and research National Center for Education Statistics.

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

\(y=6x-1 → y=0→0=6x-1→x=\frac{1}{6}\)
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 \(\frac{3}{8}\).

\(y=8x-3\) → \(x=0→y=8(0)-3 → y=-3\)

\(y=8x-3 → y=0→0=8x-3→x=\frac{3}{8}\)
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

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

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

• \(\color{blue}{y = 2x}\)

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