Question

Which Equation best represents the line graphed above?
Y=-3x-1 Y=-3x+1 Y=3x+1 Y=3x-1

Answer 1

C. y=3x+1 is the answer.

Answer 2

`y=3x+1`

Explanation:

The line has positive slope, therefore the variable in the equation must be positive (
`y=-3x+1` and
`y=-3x-1` must be discarded)

Now, in the graph we can see that the line passes over the following points:

`(0,1) \rightarrow x=0, y=1\\(1,4) \rightarrow x=1, y=4`

With the point
`(0,1)`, we can discard
`y=3x-1` because:

in the equation
`y=3x-1`, we have:
`x=0 \rightarrow y=3(0)-1=0-1=-1\rightarrow y=-1`

The line doesn't pass over the point
`(0,-1)`

Therefore, the equation is
`y=3x+1`.

We can verify the answer with the points
`(0,1)` and
`(1,4)`, replacing values in the equation:

`(0,1):\\x=0\rightarrow y=3(0)+1=0+1=1\rightarrow y=1\\\\(1,4):\\x=1\rightarrow y=3(1)+1=3+1=4\rightarrow y=4`