Determine a rule for the linear function $f$ whose graph passes through the point $(2, 7 )$ and is parallel to the graph of $g (x) = 3x - 5$ Hello I am a little stuck with following question. I don't know how to find $f(x)$ for point $(2,7)$ without $x_{2}$ and $y_{2}$.  I know $f(x)= g(x)$.

Determine a rule for the linear function f whose graph
  passes through the point $(2, 7 )$ and is parallel to the graph of
  $g (x) = 3x - 5$ 

Can you please direct me to some website where i can learn about solving such questions. Thanks in advance
 A: Any two lines that are parallel have the same slopes. In other words, the slope of $f(x)$ is the same as the slope of $g(x)$.
In this problem, $g(x)$ is written in the form
$$g(x)=m_1x+b_1$$
where $m$ is the slope and $b_1$ is some other number. We are told that $m_1=3$ and $b_1=-5$. Therefore, the slope of $f(x)$ is also $3$.
We can write $f(x)$ in the same form as we did for $g(x)$:
$$f(x)=m_2x+b_2$$
Given that $m_2=m_1=3$,
$$f(x)=3x+b_2$$
Now we go to the point we are given, $(2,7)$. We can plug these values into our equation for $f(x)$:
$$7=3(2)+b_2$$
All we have to do is solve for $b_2$.

As a side note, in the question, you wrote

I know $f(x)=g(x)$.

This is not necessarily true. While both lines have the same slope, they aren't necessarily the same line (most of the time, they aren't!). We have to solve for $f(x)$ to test whether or not this is true.
A: http://www.cimt.plymouth.ac.uk/projects/mepres/book9/bk9i5/bk9_5i4.html
Note: Two parallel lines have the same slope $m$.
A line of the form $y = mx + b$ has another line $y = mx + c$ parallel to it.
A: Another approach is by using standard forms of lines. Your given line is $3x-y=5$ So any line parallel to your given line is of the form $3x-y=k$ with $k$ some real number. The line has to pass through $(2,7)$ so substitute for $x$ and $y$ to find $k=-1$ and you are done
A: The sketch-graph of the (affine) function 3x -5 is a line, L, say, with gradient 3; or with direction vector (1 , 3) The line parallel to L, passing through (2,7) is the set
                      M  =     {(2 , 7) + k(1,3)}    where k is a real number
If  (a,b) is a point in M then
                 a - 2  =  (b -7)/3   =>    b = 3a + 1
If (a ,b) is in the graph of the function f, then
                         f(a)  = b  = 3a + 1   => f  = 3x  + 1
So  M is the sketch-graph of the function  3x + 1
