Slope-Intercept:

Convert Any Linear Equation to Slope-Intercept Form of a Line

We can use the skills of solving for a variable to change any linear equation into slope-intercept form. All that is required is that we solve for \({\text{y}}\) then arrange them so that the term with \({\text{x}}\) in it comes first.

Video Source (10:29 mins) | Transcript

Remember, the key to converting a linear equation to slope-intercept form is to solve for \({\text{y}}\) using the tools we learned in PC 101 Weeks 11 and 12. Solving for a variable is used when analyzing data.

Additional Resources

Practice Problems

Change the following equations into the slope-intercept form of a line:

  1. \({\text{y}}+14=-4{\text{x}}\)

  2. \({\text{y}}{-}7 = \frac{1}{3}{\text{x}}\)

  3. \({\text{y}} + \frac{3}{8} = \frac{1}{8}{\text{x}}\)

  4. \({\text{x}}=\frac{{\text{y}}+36}{9}\)

  5. \(-6{\text{x}}{-}2{\text{y}}=-7\)

  6. \(3{\text{x}}{-}2{\text{y}}=-1\)

Solutions

  1. \({\text{y}}=-4{\text{x}}-14\)

  2. \({\text{y}}=\frac{1}{3}{\text{x}}+7\)

  3. \({\text{y}}=\frac{1}{8}{\text{x}}-\frac{3}{8}\)

  4. \({\text{y}}=9{\text{x}}-36\) (Written Solution)

  5. \({\text{y}}=-3{\text{x}}+\frac{7}{2}\) (Written Solution)

  6. \({\text{y}}=\frac{3}{2}{\text{x}}+\frac{1}{2}\)