Given that the point (1,5) is on the graph of f(x)=3x+b, decide which one from the points (-1,-1), (3,7) are on the graph of f?

According to the rule, a point belongs to the graph of a
function, if and only if it's coordinates verify the expression of the
function.

The point (1,5) is on the graph,
so:

f(1) = 5

f(1) = 3*1 +
b

3 + b = 5

We'll subtract 3
both sides:

b =
5-3

b =
2

The function is determined and it
is:

f(x) = 3x +
2

To verify if the given points belong to
the graph of f(x), we'll substitute their coordinates into the expression of the
function.

(-1,-1), (3,7)

First
we'll verify if f(-1) = -1

f(-1) = 3*(-1) +
2

f(-1) = -3 + 2

f(-1) =
-1

So, the point (-1 , -1) belongs to the graph of
f(x).

Now, we'll verify if the point  (3,7) belongs to the
graph of f(x).

f(3) = 3*3 +
2

f(3) = 9 + 2

f(3) =
11

Since the value of f(3) is not 7, but 11, the point
(3,7) doesn't belong to the graph of f(x) = 3x + 2.