How to Write the Standard Form of Linear Equations?

Open the Standard Form Calculator in full screen →

The standard form of linear equations is a way of writing linear equations. In this guide, you learn more about writing the standard form of linear equations.

How to Write the Standard Form of Linear Equations?

Tutor-style math help

Write the Standard Form of Linear Equations: what to notice and how to work it

Linear skill

Linear topics are about constant rate of change. The slope tells how fast y changes for each 1-unit change in x, and an intercept anchors the line on an axis.

What to notice first

Find the rate and one reliable point. With those two pieces, the line is determined.

Common student mistake

Do not mix up x-intercepts and y-intercepts. At an x-intercept, y = 0; at a y-intercept, x = 0.

Key formulas and cues

\(m=\frac{y_2-y_1}{x_2-x_1}\)

\(y=mx+b\)

\(y-y_1=m(x-x_1)\)

\(Ax+By=C\)

A reliable path

Find slopeUse two points, a table, or the coefficient of x in slope-intercept form.
Find an anchorUse a point or intercept so the line is in the right location.
Check directionPositive slope rises left to right; negative slope falls left to right.

Worked examples

Find slope from two points

Example: \((1,4)\) and \((3,10)\)

Change in y is 10 – 4 = 6.
Change in x is 3 – 1 = 2.
Divide rise by run.

Answer: \(m=3\)

Write slope-intercept form

Example: slope 3 and y-intercept -2

Use y = mx + b.
Put m = 3 and b = -2.
Write the line.

Answer: \(y=3x-2\)

Open pop-up practice

Try one before moving on

Try: Find the slope through \((2,1)\) and \((6,9)\).

Answer: \(m=\frac{9-1}{6-2}=2\).

Next step: do the matching worksheet or quiz while the method is still fresh, then come back and explain the first step in your own words.

A linear equation can be written in various forms such as the standard form, the slope-intercept form, and the point-slope form. The standard form of linear equations is also known as the general form.

A step-by-step guide to the standard form of linear equations

The equation in which the highest power of the variable is \(1\) is called the linear equation or the one-degree equation. The standard form of the linear equation is shown as follows:

\(\color{blue}{Ax + By = C}\)

where \(A, B\), and \(C\) are integers, and the letters \(x\) and \(y\) are the variables.

The standard form of linear equations in one variable

A linear equation in one variable means that the equation contains only one variable. That is, this linear equation has one solution to it. The standard form or general form of linear equations in one variable is written as follows:

\(\color{blue}{Ax + B = 0}\)

Where:

\(A\) and \(B\) are integers
\(x\) is the single variable

The standard form of linear equations in two variables

When a linear equation has two variables, it has two solutions. The standard form of linear equations (a general form of linear equations) in two variables is expressed as follows:

\(\color{blue}{Ax+By=C}\)

Where:

\(A, B\), and \(C\) are integers
\(x\) and \(y\) are the variables