Is -2x plus y equals 3 a function?

Answer 1

To be a function, every x has only one y. Meaning that the y's CAN repeat for different x's, but the x's CANNOTrepeat for different y's.

To prove that -2x+y=3 is a function or not, you might first want to make the equation into y= form.

-2x+y=3

y=2x+3 ;Add 2x to both sides, on the left it cancels

Now, to prove it, you need to either graph it or plug in x's into the equation and find out if any x's ever produce more than one y-value. If you do plug in an x, and you get, let's say, 2 y's, then it is NOT a function.

If you graph it, then you can find out if it is a function or not by performing the line test. Which means that on your graph, draw a vertical line down. If at any time your line crosses two points, then it is not a function.

y=2x+3 looks like an upward sloping line, however. So it does pass the vertical line test. Therefore, it is a function.

Answer 2

Yes.

y = 2x + 3 is a linear function, meaning that, if you were to plot the function on a graph, it would create a straight line.