Cool Down
On the same coordinate grid:
- Partner A draws a vertical line, and Partner B draws a horizontal line.
- Each partner labels their line with its equation in slope-intercept form.
Pass your paper to your partner. Check your partner’s graph and equation.
Explain if your partner graphed the equation correctly and labeled the line with the correct equation.
Compare your answer:
Your answer may vary, but here is a sample.
- Partner A’s equation is of the form
- and is a vertical line. The graph and equation were correct.
- Partner B’s equation is of the form and is a horizontal line. The graph and equation were correct.
For question 2, complete the following tasks:
- Draw a point on your partner’s paper that is not on the line.
- Label the point P.
- Draw a line parallel to the original line through point .
What is the equation of the line that passes through point and is parallel to your partner’s original line?
Compare your answer:
Your answer may vary, but here is a sample.
The equation of your line will depend on where you drew it on the coordinate grid, but it should have the same slope (0 or undefined) as the first equation.
Draw a line perpendicular to the original line that goes through point . What is the equation of the line that passes through point and is perpendicular to your partner’s original line?
Compare your answer:
Your answer may vary, but here is a sample.
The equation of your line will depend on where you drew it on the coordinate grid, but it should have a slope that is not the same as the first equation.
Activity Synthesis
The purpose of the discussion is to elicit conversation about equations of lines parallel or perpendicular to horizontal or vertical lines.
- “What do you notice about the equations of vertical lines?” (They are of the form .)
- “What do you notice about the equations of lines perpendicular to vertical lines?” (They are of the form .)
- “What do you notice about the equations of horizontal lines?” (They are of the form .)
- “What do you notice about the equations of lines perpendicular to horizontal lines?” (They are of the form .)