To solve such problems we need to know about the Linear function.
A.) y – 2 = –5(x – 2)
B.) x + 7 = –4(x + 8)
C.) y – 3 = y(x + 4)
D.) y + 9 = x(x – 1)
A linear function is a function that is in the form of y=mx+c. thus we will check which functions are in this form, to know that a function is linear or not.
A.) y – 2 = –5(x – 2)
[tex]y-2=-5(x-2)\\y-2= -5x+10\\y = -5x+10+2\\y = -5x+12[/tex]
As we can that the function is in the form of y=mx+c. therefore, the function is a linear function.
B.) x + 7 = –4(x + 8)
[tex]x+7 = -4(x+8)\\x+7 = -4x-32\\4x + x = -32-7\\5x = -39[/tex]
As we can that the function is not in the form of y=mx+c. therefore, the function is a non-linear function.
C.) y – 3 = y(x + 4)
[tex]y-3=y(x+4)\\y-3=yx+4y\\[/tex]
As we can that the function is not in the form of y=mx+c. therefore, the function is a non-linear function.
D.) y + 9 = x(x – 1)
[tex]y+9 = x(x-1)\\y+9 = x^2 -x\\[/tex]
As we can that the function is not in the form of y=mx+c. therefore, the function is a non-linear function.
Learn more about Linear function:
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