Lesson 11Equations of All Kinds of Lines
Learning Goal
Let’s write equations for vertical and horizontal lines.
Learning Targets
I can write equations of lines that have a positive or a negative slope.
I can write equations of vertical and horizontal lines.
Warm Up: Which One Doesn’t Belong: Pairs of Lines
Problem 1
Which one doesn’t belong?
Activity 1: All the Same
Problem 1
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
.
Print Version
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
.
Are you ready for more?
Problem 1
Draw the rectangle with vertices
, , , . For each of the four sides of the rectangle, write an equation for a line containing the side.
Problem 2
A rectangle has sides on the graphs of
Activity 2: Same Perimeter
Problem 1
There are many possible rectangles whose perimeter is 50 units. Complete the table with lengths,
Problem 2
The graph shows one rectangle whose perimeter is 50 units, and has its lower left vertex at the origin and two sides on the axes. On the same graph, draw more rectangles with perimeter 50 units using the values from your table. Make sure that each rectangle has a lower left vertex at the origin and two sides on the axes.
Each rectangle has a vertex that lies in the first quadrant. These vertices lie on a line. Draw in this line, and write an equation for it.
What is the the slope of this line? How does the slope describe how the width changes as the length changes (or vice versa)?
Print Version
The graph shows one rectangle whose perimeter is 50 units, and has its lower left vertex at the origin and two sides on the axes. On the same graph, draw more rectangles with perimeter 50 units using the values from your table. Make sure that each rectangle has a lower left vertex at the origin and two sides on the axes.
Each rectangle has a vertex that lies in the first quadrant. These vertices lie on a line. Draw in this line, and write an equation for it.
What is the the slope of this line? How does the slope describe how the width changes as the length changes (or vice versa)?
Lesson Summary
Horizontal lines in the coordinate plane represent situations where the
Vertical lines represent situations where the