# The graphs of the functions are intersecting in a point M(x,y). Find M if f=2x/3 +8/3 and g=3x+5

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f = 2x/3 + 8/3

g = 3x + 5

M is the intersection point , to calculate m we need to solve the function:

f = g

==> 2x/3 + 8/3 = 3x + 5

==> multiply by 3:

==> 2x + 8 = 9x + 15

Group similar:

==> -7x = 7

==> x = -1

To find y we will substitutw with either f or g:

g = 3x + 5

g(-1) = 3(-1) + 5 = 2

Then the intersection point is:

M (-1, 2)

To determine the intercepting point M, we'll have to solve the system formd by the equations of the functions f and g.

The system will be:

y=2x/3 +8/3 (1)

y=3x+5 (2)

We'll solve the system using the elimination method.

We'll subtract (2) from (1):

2x/3 + 8/3 - 3x - 5 = 0

2x + 8 - 9x - 15 = 0

9x - 2x = -15+8

We'll eliminate like terms:

7x = -7

We'll divide by -7:

x = -1

We'll substitute the value of x into (2):

y=3x+5

y = -3+5

y = 2

**The intercepting point M(x,y) is the solution of the system: **

**M(-1 , 2).**

f =2x/3 +8/3and g = 2x+5.

At the intersecting point , yM = 2x/3+8/3 =3x+5

2x+8 =(3x+5)3

2x+8=9x+15

8-15 =9x-2x = 7x

x = -7/7 = -1 is the xM.

Therefore yM = 2x/3+8/3 = 2(-1)/3+8/3 = 6/3 =2

So M(x,y ) = (xM,yM) = (-1, 6)