Question

Which equation represents a linear function?

oy-2=-5(x - 2)
X+ 7 = -4(X + 8)
y - 3 = y(x + 4)
y + 9 = x(x - 1)

Answer 1

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

Explanation:

Given:

The equations given are:

`y-2=-5(x - 2)\\X+ 7 = -4(X + 8)\\y - 3 = y(x + 4)\\y + 9 = x(x - 1)`

Now, a linear function is of the form:

`y=mx+b`

Where, 'm' and 'b' are real numbers and
`m\\e0`

Equation 1:
`y-2=-5(x - 2)`

Simplifying using distributive property, we get:

`y-2=-5x+10\\y=-5x+10+2\\y=-5x+12`

The above equation is of the form
`y=mx+b`. So, it represents a linear function.

Equation 2:
`X+ 7 = -4(X + 8)`

Here, both sides of the equation has same variable 'X'. So, it will form an equation of 1 variable. So, it's not a linear function.

Equation 3:
`y - 3 = y(x + 4)`

Simplifying the above equation. This gives,

`y-3=yx+4y\\y-4y-yx=3\\y(1-4-x)=3\\y(-3-x)=3\\y=(3)/((-3-x))`

This is not of the form of the linear function. So, it is also not a linear function.

Equation 4:
`y + 9 = x(x - 1)`

Simplifying the above equation. This gives,

`y+9=x^2-x\\y=x^2-x-9`

This is not of the form of the linear function. So, it is also not a linear function.