# The graph of f is intercepting the graph of f. Find the intercepting point if f=3x-1 and g=1-3x?

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The point of intersection is where the functions meet, and the point of intesection verifies both lines:

f= 3x-1

g= 1-3x

To find where the lines intersect:

3x-1 = 1-3x

6x = 2

==> x= 2/6 = 1/3

Now let us calculate f and g :

f(3) = 3(1/3) -1 = 0

g(3) = 1-3(1/3)= 0

Then the point of intersection is (1/3,0)

f= 3x-1 and g =1-3x To find the inresection pont of the graphs.

The (x,y) coordinates for both graphs at the point of intersection are equal.

So y = 3x-1 =1-3x.

3x-1= 1-3x. add 3x.

3x+3x = 1

6x = 1

x = 1/6. Fro f=3x-1, we get f= y = 3(1/6)-1 = -1/2.

So (1/3 , -1/2) is the point of intersection.

To find the intercepting point we have to determine the common solution of the system formed by the equations of the functions f and g.

y=3x-1 (1)

y=1-3x (2)

We'll put equal (1) and (2).

3x-1 = 1-3x

We'll move all terms in x to the left side:

3x+3x-1=1

6x-1=1

We'll add 1 both sides:

6x = 1+1

6x = 2

We'll divide by 6:

x = 2/6

**x = 1/3**

Now, we'll find y:

y = 1-3x

y = 1-3*1/3

y = 1-1

**y = 0**

**The coordinates of the intercepting point are: (1/3 , 0).**