At the end of this lesson, students will be able to:
- Write an equation given slope and y–intercept.
- Write an equation given the slope and a point.
- Write an equation given two points.
- Write a linear function in slope-intercept form.
- Solve real-world problems using linear models in slope-intercept form.
Terms introduced in this lesson:
Teaching Strategies and Tips
- Allows quick identification of the slope and y−intercept. This makes graphing linear functions easier, for example.
- Written so that the dependent variable is isolated. This makes finding ordered pairs easier, for example.
Students learn to write linear equations in slope-intercept form, given:
- The slope and y−intercept of the line. See Examples 1, 2, and 7.
- The slope and any one point on the line (b is not given). See Examples 3 and 8.
- Any two points on the line (neither m nor b are given). See Examples 4 and 9.
In Example 2, have students check their answer by choosing two different points on each line and finding the slope. Construct triangles using lattice points.
Use Example 5 to demonstrate plugging an expression into a function. Encourage students to keep the parentheses with the expression as it gets plugged into the function.
Check for student conceptual understanding of function notation. For example,
f(−2)=5 is equivalent to the ordered pair (−2,5) or x=−2 and y=5.
f(0)=5 is a y−intercept. f(3)=0 is an x−intercept.
Assume that Examples 7-9 can be modeled by a linear function.
- The slope and y−intercept have contextual significance in applied problems. Have students interpret each in context of the problem.
- In applied problems, students can single out the slope from among the givens by looking for key phrases that signify a slope. For example, dollars per hour (Example 7) and inches per day (Example 8).
In Example 3b, remind students to find common denominators.