Algebra
Linear functions
Graphing linear equations
20 practice questions
2 video lessons
Theory + worked examples
Theory
There are three common ways to graph a line:
- Table: plot several \((x,y)\) points.
- Intercepts: plot the \(x\)- and \(y\)-intercepts.
- Slope-intercept: start at \(b\), then step by the slope \(m\).
Two points determine a line; a third confirms it.
Start at the \(y\)-intercept, step by the slope.
Three ways to graph.
Stepping by the slope:
\[m=\dfrac{\text{rise}}{\text{run}}\]
Plot at least two points, then draw a straight line.
How to graph a line
- Choose a method (table, intercepts, or slope-intercept).
- Find at least two points.
- Plot them.
- Draw a straight line through them.
Example 1 — By a table
Graph \(y=2x-1\) using \(x=0,1,2\).
Solution
Build points.
| \((0,-1),\ (1,1),\ (2,3)\) | \(\Rightarrow\) | \(\text{plot and connect}\) |
Example 2 — By intercepts
Graph \(y=2x-1\) using intercepts.
Solution
Find both intercepts.
| \(\text{y-int}\) | \(=\) | \(-1\) |
| \(\text{x-int}\) | \(=\) | \(\dfrac12\) |
Example 3 — By slope-intercept
Graph \(y=2x-1\) from \(m\) and \(b\).
Solution
Start at \(b=-1\); slope \(2\) means up \(2\), right \(1\).
| \(\text{from }(0,-1)\) | \(\to\) | \((1,1)\) |
Example 4 — Draw the line
How many points do you need to draw a line?
Solution
Two points determine a line, but a third checks your work.
Common pitfalls
Use at least two points; a third checks your work.
Step the slope correctly: rise then run.
Draw a straight line, extending past the points.
Frequently asked questions
How do you graph a line from slope-intercept form?
Plot the \(y\)-intercept, then step by the slope.
How many points do you need?
Two, but plotting a third checks your line.
What is the easiest method with intercepts?
Plot the \(x\)- and \(y\)-intercepts and connect.
Should the line extend past the points?
Yes — a line continues in both directions.
More in Linear functions