Question

Which equation represents a linear function? y(x – 1) = 9 y – 5 = x(–x + 2) y(y – 1) = x + 25 y – 5 = x – 20

Answer 1

The linear function: y = mx + b.

y(x - 1) = 9 → xy - y = 9 NOT (xy)

y - 5 = x(-x + 2) → y - 5 = -x² + 2x NOT (x²)

y(y - 1) = x + 25 → y² - y = x + 25 NOT (y²)

y - 5 = x - 20 → y = x - 15 YES

Answer 2

option D is linear

Explanation:

`y(x - 1) = 9`

divide both sides by x-1

`y=(9)/(x-1)` . It represents a rational function

`y - 5 = x(-x + 2)`

Multiply x inside the parenthesis

`y - 5 =-x^2 + 2x`

add 5 on both sides

`y=-x^2 + 2x+5`. It is a quadratic function because we have x^2.

`y(y - 1) = x + 25`

multiply y inside the parenthesis.

`y^2-y = x + 25`. It is a quadratic function because it has y^2

`y - 5 = x - 20`

add 5 on both sides to get y alone

`y= x-15`

The equation is in the form of y=mx +b . so it is Linear