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

Answer:

option D is linear

Step-by-step explanation:

$y(x - 1) = 9$

divide both sides by x-1

$y=\frac{9}{x-1}$ . 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