How to Convert a Linear Equation in Standard Form to Slope-Intercept Form?

The standard form and slope-intercept form are ways of writing linear equations. In this guide, you learn more about converting standard form to slope-intercept form.

How to Convert a Linear Equation in Standard Form to Slope-Intercept Form?

The equation with the highest degree \(1\) is known as the linear equation. There are different formulas available to find the equation of a straight line. 

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Step by step guide to converting standard form to slope-intercept form

The equation of a line is the equation that is satisfied by each point that lies on that line. There are several ways to find this equation in a straight line, as follows:

  • Slope-intercept form
  • Point slope form
  • Two-point form
  • Intercept form

Standard form

The standard form of linear equations is also known as the general form and is represented as:

\(Ax+By=C\)

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

Slope-intercept form

The slope-intercept form of a straight line is used to find the equation of a line. For the slope-intercept formula, we need to know the slope of the line and the intercept cut by the line with the \(y\)-axis. Let’s consider a straight line of slope \(m\) and \(y\)-intercept \(b\). The slope-intercept form equation for a straight line with a slope, \(m\), and \(b\) as the \(y\)-intercept can be given as \(y=mx + b\).

Converting standard form to slope-intercept form

By rearranging and comparing, we can convert the equation of a line given in the standard form to slope-intercept form. We know that the standard form of the equation of a straight line represents as follows:

\(Ax + By + C = 0\)

Rearranging the terms to find the value of \(y\), we get,

\(B×y=-Ax – C\)
\(y = (-\frac{A}{B})x + (-\frac{C}{B})\)

where, \((-\frac{A}{B})\) makes the slope of the line and \((-\frac{C}{B})\) is the \(y\)-intercept.

Converting Standard Form to Slope-Intercept FormExample 1:

Write the following standard form equation of a line in slope-intercept form. \(x-2y=-6\)

Solution:

Subtract \(x\) from each side. 

\(-2y = -x-6\)

Multiply each side by \(-1\).

\(2y = x + 6\)

Divide each side by \(2\). 

\(y = \frac{(x + 6)}{2}\)

\(y=\frac{x}{2}+\frac{6}{2}\)

\(y=\frac{x}{2}+ 3\)

Exercises for Converting Standard Form to Slope-Intercept Form

Write the standard form equation of a line in slope-intercept form.

  1. \(\color{blue}{7x-2y=5}\)
  2. \(\color{blue}{2x-6y=-11}\)
  3. \(\color{blue}{3x-3y=12}\)
  4. \(\color{blue}{12x-12y=5}\)
This image has an empty alt attribute; its file name is answers.png
  1. \(\color{blue}{y=\frac{7}{2}x-\frac{5}{2}}\)
  2. \(\color{blue}{y=\frac{1}{3}x+\frac{11}{6}}\)
  3. \(\color{blue}{y=x-4}\)
  4. \(\color{blue}{y=x-\frac{5}{12}}\)

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