Unit 3, Lesson 12
Equations of All Kinds of Lines
Grade 8
12.1
Warm-up
Which three go together? Why do they go together?
Graph A of four graphs labeled A, B, C, D. Graph A, two parallel lines with negative slope.
Graph B of four graphs labeled A, B, C, D. Graph B, two non parallel lines with positive slope.
Graph C of four graphs labeled A, B, C, D. Graph cC two parallel lines with slope of 0.
Graph D of four graphs labeled A, B, C, D. Graph D, two parallel lines with positive slope.
12.2
Activity
- Plot at least 10 points whose -coordinate is -4. What do you notice about them?
- Which equation makes the most sense to represent all of the points with -coordinate -4? Explain how you know.
- Plot at least 10 points whose -coordinate is 3. What do you notice about them?
- Which equation makes the most sense to represent all of the points with -coordinate 3? Explain how you know.
- Graph the equation .
- Graph the equation .
12.3
Activity
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There are many possible rectangles whose perimeter is 50 units. Complete the table with lengths, , and widths, , of at least 10 such rectangles.
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On the graph, plot the length and width of rectangles whose perimeter is 50 units using the values from your table. Using a straightedge, draw the line that passes through these points.
quadrant 1 of coordinate grid, origin o. Horizontal axis 0 to 25 by 5's. vertical axis 0 to 25 by 5's. line segment drawn from 0 comma 15 to 10 comma 15. another line segment drawn from 10 comma 15 to 10 comma 0. -
What is the slope of this line? What does the slope mean in this situation?
- Write an equation for this line.
Student Lesson Summary
Horizontal lines in the coordinate plane represent situations where the -value doesn’t change at all while the -value changes.
The horizontal line that goes through the point can be described by saying that “for all points on the line, the -value is always 3.” Since horizontal lines are neither increasing or decreasing, they have a slope of 0, and so an equation for this horizontal line is , or just .
Vertical lines in the coordinate plane represent situations where the -value doesn’t change at all while the -value changes.
The vertical line that goes through the point can be described by saying that “for all points on the line, the -value is always -2.” An equation that says the same thing is .
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