Graphing Lines Using Slope–Intercept Form

Graphing Lines 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:
    \(y=mx+b\)

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 \(6\).

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

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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