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.
Terms introduced in this lesson:
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.
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=32. 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.