Question

NEED NOW!!!

Which equation represents a linear function?
y – 2 = –5(x – 2)
x + 7 = –4(x + 8)
y – 3 = y(x + 4)
y + 9 = x(x – 1)

Answer 1

The first one: y - 2 = -5(x - 2)

Explanation:

Answer 2

the function y – 2 = –5(x – 2) is linear.

Explanation:

We need to find the correct option from provided options which represents a linear function

Since, the linear equation is in the form of y=mx+c where m is slope of line.

In first part y – 2 = –5(x – 2)

Simplify, the function

`y -2 = -5x + 10`

Add both the sides by 2, in above equation

`y = -5x +12`

This function is in the form of y=mx+c

so, this is a linear function

In second part x + 7 = –4(x + 8)

Simplify, the function

`x+7= -4x+32`

subtract both the sides by 7, in above expression

`x= -4x+32-7`

`x= -4x+25`

add both the sides by 4x,

`x +4x= 25`

`5x= 25`

divide both the sides by 5,

`x =5`

This is not in the form of y=mx+c

so, this is not a linear function

In third part y – 3 = y(x + 4)

Simplify, the function

`y-3= yx+4y`

add both the sides by 3,

`y= yx+4y+3`

This is not in the form of y=mx+c

so, this is not a linear function

In fourth part y + 9 = x(x - 1)

Simplify, the function

`y+9= x^(2)-x`

subtract both the sides by 9,

`y= x^(2)-x-9`

This is not in the form of y=mx+c

so, this is not a linear function

Therefore, the function y – 2 = –5(x – 2) is linear.