Question

If y−4=2x , which of the following sets represents possible inputs and outputs of the function, represented as ordered pairs?

a) (2,1),(4,2),(6,3)
b) (1,2),(2,4),(3,6)
c) (4,0),(6,1),(8,2)
d) (0,4),(1,6),(2,3)

Answer 1

The equation y - 4 = 2x can be rewritten as y = 2x + 4. By substituting different x values into the equation, we can determine the corresponding y values. Only set d) (0,4),(1,6),(2,3) satisfies the equation.

Step-by-step explanation:

The equation given is y - 4 = 2x. To represent the possible inputs and outputs as ordered pairs, we need to solve the equation for y in terms of x. Adding 4 to both sides of the equation, we get y = 2x + 4. Now we can substitute different x values to find the corresponding y values. Let's take a look at the options:

1. a) (2,1),(4,2),(6,3)
2. b) (1,2),(2,4),(3,6)
3. c) (4,0),(6,1),(8,2)
4. d) (0,4),(1,6),(2,3)

Let's substitute the x values from each set into the equation to find the corresponding y values:
a) For x = 2, y = 2(2) + 4 = 8, not 1. This set is not correct.
b) For x = 1, y = 2(1) + 4 = 6, not 2. This set is not correct.
c) For x = 4, y = 2(4) + 4 = 12, not 0. This set is not correct.
d) For x = 0, y = 2(0) + 4 = 4, which matches. For x = 1, y = 2(1) + 4 = 6, which matches. For x = 2, y = 2(2) + 4 = 8, which matches. Therefore, the correct answer is set d) (0,4),(1,6),(2,3).