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Do the following equations represent a linear or non-linear relationship? How do you know this?

T = 16 + 2h S = n2 + 9

Do the following equations represent a linear or nonlinear relationship How do you know this T 16 2h S n2 9 class=

Respuesta :

Answer:

They both represent linear relationships

Step-by-step explanation:

A linear equation is an equation that is in the form y = mx + c where m is the slope of the equation and c is the y-intercept.

[tex]T = 16+2h[/tex]

[tex]T[/tex] in this case represents y

[tex]16[/tex] in this case represents c (the y-intercept)

[tex]2h[/tex] in this case represents mx (the slope of the equation)

We can rearrange this equation to get it in the form [tex]T=2h+16[/tex] which is now in the form [tex]y=mx+c[/tex] therefore it is a linear equation

[tex]S=n^{2} +9[/tex]

[tex]S[/tex] in this case represents y

[tex]9[/tex] in this case represents c (the y-intercept)

[tex]n^{2}[/tex] in this case represents mx (the slope of the equation)

This equation is already in the form [tex]y=mc+c[/tex] and therefore it is a linear equation

reinhard10158

Step-by-step explanation:

I don't know "demos", but that is severely wrong.

only, if you use a coordination grid, where the x and y axis are drawn to a squared scale. there y = x² + 9 looks like a straight line. but that is an illusion.

again, linear means it is a straight line.

in the formula/equation you see this that the exponent of any x-term is 1.

if the equation contains any term of x with an exponent different to 1, or it uses special functions on x (like sin, cos, log, ...), it is not linear.

so,

S = n² + 9

you can rename this to the regular variable names

y = x² + 9

is non-linear.

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