Answer:
The intersection is
.
The Problem:
What is the intersection point of
and
?
Step-by-step explanation:
To find the intersection of
and
, we will need to find when they have a common point; when their
and
are the same.
Let's start with setting the
's equal to find those
's for which the
's are the same.

By power rule:

Since
implies
:

Squaring both sides to get rid of the fraction exponent:

This is a quadratic equation.
Subtract
on both sides:


Comparing this to
we see the following:



Let's plug them into the quadratic formula:




So we have the solutions to the quadratic equation are:
or
.
The second solution definitely gives at least one of the logarithm equation problems.
Example:
has problems when
and so the second solution is a problem.
So the
where the equations intersect is at
.
Let's find the
-coordinate.
You may use either equation.
I choose
.

The intersection is
.
factor by finding a common number you can divide both by
8p-12 and both can be divided by highest number of 4
4(2p-3) that's it
<h3>
<u>Explanation</u></h3>
We have the given slope value and the coordinate point that the graph passes through.

where m = slope and b = y-intercept. Substitute the value of slope in the equation.

We have the given coordinate point as well. After we substitute the slope, we substitute the coordinate point value in the equation.

<u>Solve</u><u> </u><u>the</u><u> </u><u>equation</u><u> </u><u>for</u><u> </u><u>b-term</u>

The value of b is 6. We substitute the value of b in the equation.

We can also use the Point-Slope form to solve the question.

Given the y1 and x1 = the coordinate point value.
Substitute the slope and coordinate point value in the point slope form.

<u>Simplify</u><u>/</u><u>Convert</u><u> </u><u>into</u><u> </u><u>Slope-intercept</u>

<h3>
<u>Answer</u></h3>
<u>
</u>
Total is $18.72 so the shopper would need to buy 6 of the 8 packs!!!