Question

For the relation: y=1/4 x-4, sketch the graph of the relation and its inverse, then write the equation for the inverse.Inverse: y=

Answer 1

Step-by-step explanation

In this problem, we have the relation:

`y=(1)/(4)\cdot x-4.`

(1) This function is a line with:

• slope m = 1/4 (it increases 1 unit on the y-axis for every 4 units on the x-axis),

,

• y-intercept b = -4.

(2) Now, to find the inverse, we solve the equation for x in terms of y:

`\begin{gathered} y=(1)/(4)x-4, \\ y+4=(1)/(4)x, \\ x=4(y+4), \\ x=4y+16. \end{gathered}`

Now, we interchange x and y:

`y=4x+16.`

This function is a line with:

• slope m = 4 (it increases 4 units on the y-axis for every unit on the x-axis),

• y-intercept b = 16.

(3) Plotting both functions, we get the following graph:

Answer

The inverse of the function is:

`y=4x+16`

To plot the lines, we use the following points:

• for the original function: (-5, -4) and (-4, 0)

,

• for the inverse function: (-4, -5) and (0, -4).

Graph of the function and its inverse: