Concept Byte: Investigating y = mx + b

Use With Lesson 5-3

TECHNOLOGY

You can use a graphing calculator to explore the graph of an equation in the form y = m x + b . y equals m x plus b .  For this activity, choose a standard screen by pressing zoom begin box , zoom , end box  6.

1. Graph these equations on the same screen. Then complete each statement.

   y = x + 3 y equals x plus 3

   y = 2 x + 3 y equals 2 x plus 3

   y = 1 2 x + 3 y equals , 1 half , x plus 3

   1. The graph of ? is steepest.
   2. The graph of ? is the least steep.

2. Match each equation with the best choice for its graph.

   1. y = 1 4 x − 2 y equals , 1 fourth , x minus 2
   2. y = 4 x − 2 y equals 4 x minus 2
   3. y = x − 2 y equals x minus 2
   1. 
   2. 
   3. 

3. Graph these equations on the same screen.

   y = 2 x + 3 y equals 2 x plus 3

   y = − 2 x + 3 y equals negative 2 x plus 3

   How does the sign of m affect the graph of the equation?

4. Reasoning How does changing the value of m affect the graph of an equation in the form y = m x + b ? y equals m x plus b question mark

5. Graph these equations on the same screen.

   y = 2 x + 3 y equals 2 x plus 3

   y = 2 x − 3 y equals 2 x minus 3

   y = 2 x + 2 y equals 2 x plus 2

   Where does the graph of each equation cross the y-axis? (Hint: Use the ZOOM feature to better see the points of intersection.)

6. Match each equation with the best choice for its graph.

   1. y = 1 3 x − 3 y equals , 1 third , x minus 3
   2. y = 1 3 x + 1 y equals , 1 third , x plus 1
   3. y = 1 3 x y equals , 1 third , x
   1. 
   2. 
   3. 
7. Reasoning How does changing the value of b affect the graph of an equation in the form y = m x + b ? y equals m x plus b question mark

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