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# 5.3: Linear Equations in Standard Form

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 $y-$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.

## Vocabulary

Terms introduced in this lesson:

standard form
slope
intercepts

## 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 $b$ in $ax + by = c$ does not represent the $y-$intercept as it did in an equation in slope-intercept form.

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

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

Feb 22, 2012

## Last Modified:

Aug 22, 2014
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CK.MAT.ENG.TE.1.Algebra-I.5.3