MATH 101: GRAPH AND WRITE EQUATIONS AND INEQUALITIES/Graphing Lines
Module 3 – Case
Graph and Write Equations and Inequalities
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Complete the following problems using the Case 3 Answer Template. Here are some formulas and equations you will use in this section.
Slope: m = change in y = y_{2}y_{1} change in x x_{2}–x_{1}
Slopeintercept form: y = mx + b
Pointslope form: yy_{1}= m(xx_{1})
Standard form: Ax + By = C; where A is a positive value
Find the slope of the points. Reduce to lowest terms.
1. (0, 2) (4, 6)
2. (7, 3) (9, 3)
3. (5, 2) (1, 5)
4. (12, 4) (12, 6)
Identify the slope and yintercept in the following equations.
5. 2x+3y=8
6. 6x=y+1

Write an equation of a vertical line passing through the point (6, 3).

Write an equation of a horizontal line passing through the point (2, 8).

Write an equation of a line in slopeintercept form with a slope of 4 and passing through the point (0, 3).

Write an equation of a line in slopeintercept form with a slope of 1/2 and passing through the point (0, 6).

Write an equation of a line in pointslope form with a slope of 3/4 and passing through the point (1, 5).

Write an equation of a line in standard form with a slope of 8 and passing through the point (10, 2).

Write an equation of a line passing through the points (2, 1) and (0, 4). Write the final answer in slopeintercept form.

Write an equation of a line passing through the points (3, 6) and (5, 3). Write the final answer in slopeintercept form.
Graph the following equations and inequalities on a coordinate plane, shading the solution set where necessary.
Note: When completing this assignment in the Case 3 Answer Template, go to “insert” and “shapes.” Choose the circles for the points and the lines to connect the dots. Use the arrows to represent the shading.
For example:
15. y= 4x2
16. 2x+5y=10
17. x=3 and y=6
18. 3x+5y ≤ 15
19. y < 2x3
20. x > 4 and y ≤ 1
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Module 3 – SLP
Graph and Write Equations and Inequalities
Complete the following problems using the SLP 3 Answer Template. Here is a formula and equation you will use in this section.
Write the final answer in the terms being asked such as dollars/cents, degrees, tickets, etc.
Slope: m= change in y = y_{2}y_{1}
change in x x_{2}x_{1}
Slopeintercept form: y=mx+b
1. Your monthly commission as an appliance sales person is represented by the equation, S = 50x+450, where 50 is the rate paid for each appliance sold, x is the number of appliances sold, 450 is the base pay per month, and S is the salary. Complete the following table to represent your total salary for x appliances sold. Show your work for each one.
x 
14 
22 
25 
40 
51 
S 






You are offered the option of choosing a yearly salary of $45,000 or continue working on commission.

Using the equation from problem #1, how many appliances do you have to sell per year in order to match this salary? (Hint: $450 is the base pay per month, not year. Multiply the base pay by 12 to represent a full year.)

If you currently average 74 appliance sales per month, which option should you choose?


Best Car rental agency charges a flat rate of $40 and 10¢ per mile to rent a standard car. A+ Rentals charges a flat rate of $35 and 20¢ per mile for the same car.

Write an equation to represent the total cost (y) and number of miles (x) of renting from each company.

If you plan to rent a car and travel 500 miles, which plan would you choose and why? Show your work.

How many miles do you need to drive for both plans to cost the same?


The cost of producing cell phones is represented as C=mx+b, where m is the marginal cost, x is the number of phones produced, b is the fixed cost, and C is the final cost.

If the fixed cost is $75 and the marginal cost is $8, write the cost equation.

In March, the total cost was $18,955. Calculate the number of phones produced using the equation.

If the goal for March was to produce at least 2,000 phones, did the company meet this goal? Show mathematically the number of phones by which the company exceeded or missed the goal.


Tim works parttime at a retail store. His salary varies directly by the number of hours worked. Last week he earned $99.45 for 13 hours of work. This week he earned $160.65.

Write and solve an equation that represents this scenario.

How many hours did he work?


Three years after purchase, a car is estimated to be worth $24,000. At five years, its value is $19,000. If the car is depreciating in a linear manner, write an equation that represents the depreciation of the car. Answer the following questions:

How much is the car depreciating each year?

What was the purchase price of the car?

If the car continues this rate of depreciation, what will its value be at year 10?


On a particular April day, the temperature at 8 a.m. was 40°F. By 4 p.m. the temperature was 64°F. What was the hourly rate of temperature change?

The cost for an electrician is $135 for 3 hours. A 7hour repair costs $315. Showing your calculations, determine the price of a 12hour repair.

Sarah has two parttime jobs and needs to earn at least $300 total per week. Job A pays her $10 an hour and job B pays $7.50 an hour. Write an inequality that represents this scenario. Name and label your variables, such as Job A= x.

A manufacturer produces a 4cup and 8cup coffee maker. The 4cup maker takes 6 hours to produce and the 8cup takes 9 hours. The manufacturer has at most 500 hours of labor per week.

Write an inequality to represent the number of each type of coffee makers they can produce in a week.

Is it possible to produce 20 4cup and 30 8cup coffee makers in a given week? Explain why or why not showing all of your calculations.
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Graphing Lines
What are the 3 methods to graph a line? Choose 1 of the methods and describe how to graph a line using an example equation? Why do you prefer this method?
Create 1 equation and ask your peers to describe the graph using 1 of the 3 methods. Return to the discussion to check your peers’ understanding and offer help as needed. Be sure to post the answer at the close of the module.

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