How to Graph Lines by Using Slope–Intercept Form

How to Graph Lines by Using Slope–Intercept Form

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

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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

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

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