Explanation
In this problem, we have the relation:
[tex]y=\frac{1}{4}\cdot x-4.[/tex]
(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:
[tex]\begin{gathered} y=\frac{1}{4}x-4, \\ y+4=\frac{1}{4}x, \\ x=4(y+4), \\ x=4y+16. \end{gathered}[/tex]
Now, we interchange x and y:
[tex]y=4x+16.[/tex]
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:
[tex]y=4x+16[/tex]
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:
