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

1 Answer
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)#