Answer:
[tex]y=3x+1[/tex]
Step-by-step explanation:
The line has positive slope, therefore the variable in the equation must be positive ([tex]y=-3x+1[/tex] and [tex]y=-3x-1[/tex] must be discarded)
Now, in the graph we can see that the line passes over the following points:
[tex](0,1) \rightarrow x=0, y=1\\(1,4) \rightarrow x=1, y=4[/tex]
With the point [tex](0,1)[/tex], we can discard [tex]y=3x-1[/tex] because:
in the equation [tex]y=3x-1[/tex], we have: [tex]x=0 \rightarrow y=3(0)-1=0-1=-1\rightarrow y=-1[/tex]
The line doesn't pass over the point [tex](0,-1)[/tex]
Therefore, the equation is [tex]y=3x+1[/tex].
We can verify the answer with the points [tex](0,1)[/tex] and [tex](1,4)[/tex], replacing values in the equation:
[tex](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[/tex]
