Graphing Lines Using Standard Form

Graphing Lines Using Standard Form

Learn how to graph lines by using the equation of the line in standard form.

Step by step guide to graphing lines using the standard form

  • Find the \(x\)-intercept of the line by putting zero for \(y\).
  • Find the \(y\)- intercept of the line by putting zero for the \(x\).
  • Connect these two points.

Example 1:

Sketch the graph of \(x-y=\ – 2\)

Solution:

First isolate \(y\) for \(x: x-y=-2→y=x+2\)
Find the \(x\)−intercept of the line by putting zero for \(y\).
\(y=x+2→x+2=0→x=-2 \)
Find the (y)−intercept of the line by putting zero for the \(x\).
\(y=0+2→y=2 \)
Then: \(x\)−intercept: \((-2,0)\) and \(y\)−intercept: \((0,2)\)

Example 2:

Sketch the graph of \(x-y= \ -5\).

Solution:

First isolate \(y\) for \(x: x-y=-5→y=x+5\)
Find the \(x−\)intercept of the line by putting zero for \(y\).
\( y=x+5→x+5=0→x=\ -5 \)
Find the \(y−\)intercept of the line by putting zero for the \(x\).
\(y=0+5→y=5\)
Then: \(x−\)intercept: \((-5,0)\) and \(y−\)intercept: \((0,5)\)

Exercises

Sketch the graph of each line.

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

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