Math 101: graph and write equations and inequalities/graphing lines

 

Module 3 – Case

 

Graph and Write Equations and Inequalities

 

Assignment Expectations

 

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 = y2-y1
                   change in x    x2–x1

 

Slope-intercept form:  y = mx + b

 

Point-slope form:  y-y1= m(x-x1)

 

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 y-intercept in the following equations.

 

5. 2x+3y=8

 

6. 6x=y+1

 

 

 

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

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

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

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

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

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

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

  8. Write an equation of a line passing through the points (-3, 6) and (-5, 3). Write the final answer in slope-intercept 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= 4x-2

 

16.  2x+5y=10

 

17.  x=3 and y=6

 

18.  3x+5y ≤ 15

 

19.  y < -2x-3

 

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 = y2-y1
                  change in x     x2-x1

 

Slope-intercept 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.

 

 

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

    1. 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.)

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

  2. 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. 

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

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

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

  3. 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. 

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

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

    3. 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.

  4. Tim works part-time 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. 

    1. Write and solve an equation that represents this scenario.

    2. How many hours did he work?

  5. 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:

    1. How much is the car depreciating each year?

    2. What was the purchase price of the car?

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

  6. 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?   

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

  8. Sarah has two part-time 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.

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

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

    2. Is it possible to produce 20 4-cup and 30 8-cup 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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