Kerry has been a teacher and an administrator for more than twenty years. She has a Master of Education degree.
After this lesson, students will be able to:
- define standard form
- convert linear equations from slope-intercept to standard form
- solve linear equations
This lesson will take approximately 45-90 minutes.
Solve linear equations in one variable.
Analyze and solve pairs of simultaneous linear equations.
- linear equation
- slope-intercept form
- standard form
Materials needed: graph paper, chart paper, markers
Activate prior knowledge by writing 700,000 + 40,000 + 3,000 + 200 + 90 + 4 on the board. Remind students that this is an example of expanded notation and ask them to write the same number in standard form. Ask them why the same number might be written in more than one form. After listening to their responses, explain that the same linear equation can also be written in different forms for different reasons.
Watch the lesson Linear Equations: Intercepts, Standard Form and Graphing as a class. Pause at 1:45.
Write down the equation y = 2x + 9. Tell students to turn and talk to a partner about how to change this equation from slope-intercept form to standard form. Allow a couple of pairs to share how they got the answer.
Write down the equation y = 4x + 7. Have students convert the equation to standard form independently and then check their answer with a partner.
Continue watching the video. Pause at 3:43. Ask students the following question:
- What is the advantage of having a linear equation in slope-intercept form?
Write down the equation 2x + 4y = 8. Have students convert the equation to slope-intercept form and graph. Have students explain to a partner how they solved the problem.
Write down the equation x + 3y = 12. Have students find a new partner to solve the equation with. Have students graph their answer. Provide pairs with an opportunity to share. Make sure students are able to justify their answers.
Watch the remainder of the video with students. Ask:
- What is the advantage of using standard form?
Write down the equation 2x + 4y = 8 again. This time, have students work with their partner to find the intercepts without converting it into slope-intercept form. Have students graph the equation.
Have students work independently to find the intercepts and graph the equation x + 3y = 12 from standard form.
Divide students into small groups. Provide each group with chart paper and markers.
Write the equation 5x + 2y = 8 on the board.
Have groups create a poster that explains how to solve and graph this equation by converting it into slope-intercept form and how to graph the equation by finding the intercepts from standard form. Have students explain why both are the same in mathematical terms.
Use the lesson's printable worksheet to check for understanding.
- Read a word problem to students, such as, 'A car rental costs $35 for the first day and $25 for each additional day. Write a linear equation in standard form that describes this scenario. Then, graph it.
- After solving the problem, have students write their own word problems that can be written as linear equations.
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