Is y=2x +5 a direct variation and if so, what is the constant?

1 Answer
Alan P.
Oct 1, 2015

y=2x+5 is not a direct variation

Explanation:

To be a direct variation, multiplying either variable by some amount must cause the other variable to be multiplied by exactly the same amount.

For the example y=2x+5
We can see that if x=color(blue)(2) then y=color(green)(9)

If we multiplied x by color(red)(3) (i.e. x=color(blue)(2)xxcolor(red)(3)=color(brown)(6))
then
if x and y were in direct variation
the value of y would need to become color(green)(9)xxcolor(red)(3)=color(purple)(21)

but we can see that y=2*(color(brown)(6)) + 5 = 17 !=color(purple)(21)

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