Is #y = 2x + 5# a direct variation and if so, how do you find the constant?

Yes, it is direct variation. The constant is 2

A direct variation always gives a straight line graph and can be expressed as y =ax + b where a and b are constants. a represents the slope of the line - the bigger it's value the steeper the slope. b is the value of y when x = 0 and is therefore where the line crosses the vertical axis. b is the value normally referred to as the constant and a as the slope. Therefore in this case the constant is 5.

No, ( y = 2x + 5 ) is not a direct variation because it doesn't follow the form ( y = kx ). In direct variation equations, the variable ( y ) is directly proportional to the variable ( x ), with a constant of proportionality represented by ( k ). If ( y = 2x + 5 ) were a direct variation, it would be in the form ( y = kx ), where ( k ) is the constant of proportionality. However, in this equation, the term ( 5 ) is added to ( 2x ), indicating that the relationship between ( x ) and ( y ) is not directly proportional.