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