Q61. - Algebra 2

Question

Answer the question that was posed at the beginning of the lesson.

 

How do linear equations relate to time spent studying?

 

Include the following in your answer:

why only the part of the graph in the first quadrant is shown, and

an interpretation of the graph's intercepts in terms of the amount of time

Lolita spends on each subject.

Step-by-Step Solution

Answer

The time variable is the independent variable; time spent on studying is a dependent variable.

So, the relation between the time and the studying will give a linear relation, as more time spent on study gives you best results and as less time spent on studies gives you fewer results

Step 1 – Describe how the linear equations relate to time spent studying.

Given that $x\text{ and }y$are the time spent on each subject math and chemistry respectively.

A total hour that Lolita has to do homework is 4 hours.

The equation related to these variables is $x+y=4$.

 

The time variable is the independent variable; time spent on studying is a dependent variable.

So, the relation between the time and the studying will give a linear relation, as more time spent on study gives you best results and as less time spent on studies gives you lesser results.

Step 2 – Graphical interpretation of the equation x + y = 4 :

The graph is in the first quadrant, because the time cannot be negative and time spent on studies also cannot be negative.

So, both variables should be positive only.

 

From the graph, the $x-$intercept is $\left(4,0\right)$, this $x-$intercept gives the information that the total 4 hours time is spent on math only, and 0 hours spent on chemistry.

 

From the graph, the $y-$intercept is $\left(0,4\right)$, this x-intercept gives the information that the total 4 hours time is spent on chemistry only, and 0 hours spent on math.

Step 3 – Describe the interpretation of the graph's intercepts in terms of the amount of time Lolita spends on each subject

From the graph, the $x-$intercept is $\left(4,0\right)$, this $x-$intercept gives the information that the total 4 hours time is spent on math only, and 0 hours spent on chemistry.

 

From the graph, the $y-$intercept is $\left(0,4\right)$, this $y-$intercept gives the information that the total 4 hours time is spent on chemistry only, and 0 hours spent on math