Question

Choose a linear function for the line represented by the point-slope equation y – 5 = 3(x – 2). f(x) = 3x + 1 f(x) = 3x – 1 f(x) = 8x + 10 f(x) = 8x – 10

Answer 1

Answer: f(x) = 3x - 1

Explanation:

y - 5 = 3(x - 2); now solve for y;

y = 3(x - 2) + 5; now distribute the 3 and add like terms;

y = 3x - 6 + 5

y = 3x -1 ; replace y with f(x);

f(x) = 3x - 1

Answer 2

Answer: The correct option is (B)
`y=3x-1.`

Step-by-step explanation: We are given to choose a linear function for the following line represented by the point-slope form of the equation :

`y-5=3(x-2)~~~~~~~~~~~~~~~~~~~~~~~~~~~~`(i)`

Let us consider that y = f(x). Then, all the terms containing x and the constant terms must be bought on the right-hand side.

From equation (i), we have

`y-5=3(x-2)\\\\\Rightarrow y-5=3x-6\\\\\Rightarrow y=3x-6+5\\\\\Rightarrow y=3x-1.`

Thus, the correct linear function is
`y=3x-1.`

Option (B) is CORRECT.