Answer:
the function y – 2 = –5(x – 2) is linear.
Step-by-step 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
[tex]y -2 = -5x + 10[/tex]
Add both the sides by 2, in above equation
[tex]y = -5x +12[/tex]
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
[tex]x+7= -4x+32[/tex]
subtract both the sides by 7, in above expression
[tex]x= -4x+32-7[/tex]
[tex]x= -4x+25[/tex]
add both the sides by 4x,
[tex]x +4x= 25[/tex]
[tex]5x= 25[/tex]
divide both the sides by 5,
[tex]x =5[/tex]
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
[tex]y-3= yx+4y[/tex]
add both the sides by 3,
[tex]y= yx+4y+3[/tex]
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
[tex]y+9= x^{2}-x[/tex]
subtract both the sides by 9,
[tex]y= x^{2}-x-9[/tex]
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.
