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5.3: Linear Equations in Standard Form

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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.

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