# Determine the coordinates of the intercept point of the graphs f and g. f(x) = 3x - 2 g(x)= 5x + 3

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We can find intersecting point for the function by solvind:

f= g

3x-2 = 5x + 3

group similar:

==> 2x = -5

==> x = -5/2

Now to find y-value we will substitute with either f ot g.

f(-5/2) = 3(-5/2) -2

= -15/2 - 4/2 = -19/2

Then the intercepting point is (-5/2, -19/2)

To calculate the coordinates of the intercepting point, we'll have to solve the system of equations:

y = 3x - 2 (1)

y = 5x + 3 (2)

3x - 2 = 5x + 3

We'll subtract 5x both sides:

3x - 5x - 2 = 3

-2x - 2 = 3

We'll add 2 both sides:

-2x = 3+2

-2x = 5

We'll divide by -2:

x = -5/2

We'll substitute x in (1):

y = 3*(-5)/2 - 2

y = -15/2 - 2

y = (-15-4)/2

y = - 19/2

So, the coordinates of the intercepting point are:

** (-5/2 , -19/2)**

f(x) = 3x-2 and g(x) = 5x+3

To find the intersection point of the graphs.

Solution:

At the point of intersection, the y cordinates f(x) and g(x) are equal. So 3x-2 =5x+3

-2 -3 = 5x-3x =2x

-5 = 2x. Or -5/2 =x.

x= -5/2.

y = f(x) gives: 3(-5/2) -2 = - 19/2 = -9.5

So the point of inresection : (-5/2 , -19/2) = (-2.5 , -9.5)

At the point of intersection, f(x)=g(x)

Therefore: 3x-2=5x+3 or 5x-3x=-3-2 or 2x=-5 or x=-5/2.

Substituting x=-5/2 into any of the functions we get -9.5.

So the coordinates of the point of contact if the two graphs have been plotted on the x-y plane are (-5/2, -19/2).