Verify if the lines y = 2x/3 + 8/3 and y = 3x + 5 are intercepting or they are parallel .

Since the equations are put in the standard
form:

y = mx + n

we can say
that they are not parallel.

Let's see
why?

According to the rule, 2 parallel lines have their
slopes equal.

m1 = m2

We'll
determine m1 and m2 and we'll notice that:

m1 = 2/3 and m2
= 3

They are not equal so the lines aren't
parallel.

To verify if  the lines have an intercepting
point, 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
lines have an intercepting point and the coordinates of the intercepting point,
(x,y), represent the solution of the system: (-1 ,
2).