Question

Consider the equations y = x , y = 2 3 x , and y = 2 3 x + 1 . Use transformations to complete the table of values.


X y=x y=2/3 x y=2/3x+1
-6
-3
0
3
6

Answer 1

Answer:

The table:

y = x     y = 2/3 x     y = 2/3 x + 1

-6  →       -4        →        -3

-3  →       -2        →        -1

0  →        0        →         1  

3  →        2        →         3

6  →        4        →         5

Step-by-step explanation:

- We have three equations:

1. y = x

2. y = $\frac{2}{3}$ x

3. y = $\frac{2}{3}$ x + 1

∵ Equation 2 = $\frac{2}{3}$ × equation 1

- That means we multiply the value of y by $\frac{2}{3}$

∵ $\frac{2}{3}$ < 1

∴ Equation 2 is the image of equation 1 by vertical compression with

  scale factor $\frac{2}{3}$

∵ Equation 3 = equation 2 + 1

- That means we add the value of y by 1

∴ Equation 3 is the image of equation 2 by translation 1 unit up

- To fill the table we will multiply each y value by $\frac{2}{3}$ to

  find the values of the equation 2 and then add 1 to find the values of

  equation 3

→ The 1st equation y = x

∵ x = -6 , -3 , 0 , 3 , 6

∴ y = -6 , -3 , 0 , 3 , 6

→ The 2nd equation y = $\frac{2}{3}$ x

∵ x = -6 , -3 , 0 , 3 , 6

∴ y = -4 , -2 , 0 , 2 , 4

→ The 3rd equation y = $\frac{2}{3}$ x + 1

∵ x = -6 , -3 , 0 , 3 , 6

∴ y = -3 , -1 , 1 , 3 , 5

The table:

x  →  y = x  →  y = 2/3 x  →  y = 2/3 x + 1

-6 →      -6  →       -4        →        -3

-3 →      -3  →       -2        →        -1

 0 →       0  →        0        →         1  

 3 →       3  →        2        →         3

 6 →       6  →        4        →         5