# 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?

*print*Print*list*Cite

f(x) = 3x+b

Since the point (1,5) is on f(x) , then the point shoul verify the f(x) such that f(1) = 5

==> f(1) = 3 + b = 5

==> b= 2

==> f(x) = 3x + 2

Now to verify whcih point is on f(x) we wil check if the points verift f(x):

(-1,-1)

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

**Then the point (-1, -1) in on f(x).**

(3,7)

f(3) = 3*3 + 2 = 11

**Then (3,7) does NOT belong to f(x),**

Since (1,5) is on f(x) = 3x+b, the coordinates (1,5) should satisfy f(x) = 3x+b. So,

f(1) = 5 = 3*1+b.

Therefore b = 5-3 = 2.

Therefore the equation given equation is f(x) = 3x+2

Verification of the point (- 1, -1) gives: f(-1) = -1= 3(-1)+2 = -1 is true. Therefore (-1,-1) is a point on f(x) = 3x+2.

Verification of (3,7): f(3) = 7 = 3*(3) +2 , Or 7 = 11 is not true.

Therefore (3,7) is not on the graph of f(x) = 3x+2.

We are given that the point (1,5) lies on the graph for the function f(x) = 3x + b.

So 5 = 3x + b

=> 5 = 3*1 + b

=> b = 5 - 3 = 2

So f(x) = 3x + 2

Now taking the point (-1,-1)

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

= -3 +2 =-1

Therefore ( -1,-1) lies on the graph of the function.

Next let's take (3, 7)

f(3) = 3*3 + 2 = 9 +2 =11

So (3,7) does not lie on the graph of the function.

**Only (-1, -1) lies on the graph of the function.**

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.