Algebra
Linear functions
Standard form of linear equations
20 practice questions
2 video lessons
Theory + worked examples
Theory
Standard form of a line is
\[Ax+By=C,\]
with integer \(A,B,C\) (usually \(A\ge0\)). It makes intercepts easy: set \(y=0\) for the \(x\)-intercept and \(x=0\) for the \(y\)-intercept.
Convert to slope-intercept by solving for \(y\).
\(2x+3y=6\) with intercepts \((3,0)\) and \((0,2)\).
Standard form and its intercepts.
Standard form:
\[Ax+By=C\]
Intercepts: \(y=0\) gives the \(x\)-intercept, \(x=0\) the \(y\)-intercept.
How to use standard form
- For the \(x\)-intercept, set \(y=0\).
- For the \(y\)-intercept, set \(x=0\).
- To convert, solve for \(y\).
- To write standard form, clear fractions and move terms.
Example 1 — Find the x-intercept
Find the \(x\)-intercept of \(2x+3y=6\).
Solution
Set \(y=0\).
| \(2x\) | \(=\) | \(6\) |
| \(x\) | \(=\) | \(3\) |
Example 2 — Find the y-intercept
Find the \(y\)-intercept of \(2x+3y=6\).
Solution
Set \(x=0\).
| \(3y\) | \(=\) | \(6\) |
| \(y\) | \(=\) | \(2\) |
Example 3 — Convert to slope-intercept
Write \(2x+3y=6\) as \(y=mx+b\).
Solution
Solve for \(y\).
| \(3y\) | \(=\) | \(-2x+6\) |
| \(y\) | \(=\) | \(-\dfrac23x+2\) |
Example 4 — Write in standard form
Write \(y=3x-4\) in standard form.
Solution
Move the \(x\)-term to the left.
| \(-3x+y\) | \(=\) | \(-4\) |
| \(3x-y\) | \(=\) | \(4\) |
Common pitfalls
Set \(y=0\) for the \(x\)-intercept, not \(x=0\).
Standard form uses integer coefficients.
Solve for \(y\) to reach slope-intercept form.
Frequently asked questions
What is standard form?
\(Ax+By=C\) with integer coefficients.
How do you find the x-intercept from standard form?
Set \(y=0\) and solve for \(x\).
How do you convert to slope-intercept?
Solve the equation for \(y\).
Why use standard form?
It makes both intercepts quick to find.
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