Question

Which equation represents a linear function?

Answer 1

Answer:

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

Step-by-step 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 $m\ne0$

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,

$y-3=yx+4y\\y-4y-yx=3\\y(1-4-x)=3\\y(-3-x)=3\\y=\frac{3}{(-3-x)}$

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.