We have that the line passes by the points (0, -2) & (1, 2). Using this we determine the slope (m) and then the function. After that we transformate the function. We proceed as follows:
[tex]m=\frac{2-(-2)}{1-0}\Rightarrow m=4[/tex]
Now, using one of the points [In our case we will use (0, -2), but we can use any point of the line] and the slope, we replace in:
[tex]y-y_1=m(x-x_1)[/tex]
Then:
[tex]y-(-2)=4(x-0)[/tex]
Now, we solve for y:
[tex]\Rightarrow y+2=4x\Rightarrow y=4x-2[/tex]
And we apply the transformation to our line, that is f(x) -> f(x) + 6:
[tex]y=4x-2+6\Rightarrow y=4x+4[/tex]
Therefore our final line (After the transformation) is y = 4x + 4, and graphed that is:
