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5.3: Linear Equations in Standard Form

Difficulty Level: At Grade Created by: CK-12

Learning Objectives

At the end of this lesson, students will be able to:

  • Write equivalent equations in standard form.
  • Find the slope and \begin{align*}y-\end{align*}intercept from an equation in standard form.
  • Write equations in standard form from a graph.
  • Solve real-world problems using linear models in standard form.


Terms introduced in this lesson:

standard form

Teaching Strategies and Tips

An equation in standard form:

  • Can be used to express the equation of a vertical line. This is not possible in slope-intercept or point-slope forms.
  • Makes finding intercepts easy. Remind students of the cover-up method introduced in lesson Graphing Using Intercepts, chapter Graphs of Equations and Functions.

Use Example 3 to find the equations of the lines in standard form using the intercepts and without resorting to slope. The steps are essentially the steps used in the cover-up method only in reverse.

Have students derive the equations that describe the situations in Examples 4 and 5.

Error Troubleshooting

General Tip: Point out that the \begin{align*}b\end{align*} in \begin{align*}ax + by = c\end{align*} does not represent the \begin{align*}y-\end{align*}intercept as it did in an equation in slope-intercept form.

In Example 3c, the \begin{align*}x-\end{align*}intercept is a fraction, \begin{align*}x = \frac{3} {2}\end{align*}. After eliminating the denominator, \begin{align*}2x = 3\end{align*}, proceed with the method as usual using the \begin{align*}3\end{align*} instead; i.e. What number times \begin{align*}3\end{align*} equals some other number times \begin{align*}4\end{align*} (the \begin{align*}y-\end{align*}intercept)?

General Tip: Encourage students to include units when labeling their variables.

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