Question

Which of the following points lies on the graph of the inverse of y-8=5(x+2)? Explain your choice.

a) (−2,8)
b) (2,3)
c) (0,10)
d)(5,−2)

Answer 1

By expressing the equation y - 8 = 5(x + 2) in its inverse form, isolating y, and testing each provided point against the inverse function, it's determined that option d) (5, -2) lies on the graph of the inverse.

Step-by-step explanation:

To determine which point lies on the graph of the inverse of the equation y - 8 = 5(x + 2), we first need to express the equation in its inverse form. To find the inverse of a function, we interchange the roles of x and y and solve for y. Let's start by isolating y in the original equation:

y = 5(x + 2) + 8

Now we switch x and y:

x = 5(y + 2) + 8

To isolate y, we solve this new equation:

x - 8 = 5(y + 2)

x - 8 = 5y + 10

y = (x - 18)/5

We can now test each provided point to see which one satisfies the given inverse function:

• a) (-2,8): 8 = (-2 - 18)/5 does not satisfy the equation.
• b) (2,3): 3 = (2 - 18)/5 does not satisfy the equation.
• c) (0,10): 10 = (0 - 18)/5 does not satisfy the equation.
• d) (5,-2): -2 = (5 - 18)/5; when simplified, -2 = -13/5, which is true, so d) (5, -2) lies on the inverse graph.

Therefore, option d) (5, -2) lies on the graph of the inverse function.