Purchase Solution

Applications of Graphs of Linear Equations

Not what you're looking for?

Ask Custom Question

Name: __________________________ Date: _____________

1. Which of the ordered pairs
(6, 1), (8, 0), (4, -2), (-4, 6)
are solutions for the equation x + 2y = 8?

2. A small company did a poll of how their employees commuted to work. The data is shown in the bar graph below.

(a) How many people commute to work via car?
15 people
(b) How do most of the employees commute to work?
By car

3. Complete the ordered pairs for the equation 2x + y = 10.
(5, ), ( , 10), ( , -2), (0, )

4. Find four solutions for the equation 3x + 5y = 15.

5. Graph 2x - y = 4.

6. Graph using the intercept method: x + 3y = 6.

7. Graph by first solving for y.
4x - 3y = 6

8. Graph using the intercept method: 2x + y = 4.

9. Find the slope of the line passing through the points (9, 12) and (8, 4).

10. Find the slope of the line passing through the points (-10, 10) and (0, 0).

11. Find the slope of the graphed line.

12. Find the slope of the graphed line.

13. If y varies directly with x, and y = 110 when x = 100, find the constant of variation k.

14. The following pie chart represents the results of a survey about whether people in a certain town have cats or dogs as pets.

What percentage of the people have only cats or only dogs?

15. The line graph below shows the number of stray dogs in a certain city for the years listed.

(a) Which year had the least amount of stray dogs?
(b) Between which two years did the greatest decrease in stray dogs occur?

16. A student earns $0.65 for each mistake she finds in a text. Sketch the equation of direct variation.

17. Find the slope and y-intercept.
8x + 5y = -50

18. Write the equation of the line with slope 4 and y-intercept (0, -5). Then graph the line.

19. Write the equation of the line with slope and y-intercept (0, 3). Then graph the line.

20. A line passing through (10, 4) and (-3, y) is perpendicular to a line with slope . Find the value of y.
A) -13
B) -11
C) -10
D) -8

21. An airplane covered 15 miles of its route while decreasing its altitude by 31,000 feet. Find the slope of the airplane's line of descent. Round to the nearest hundredth. [Hint: 1 mi = 5280 feet.]

22. Determine which two equations represent parallel lines.
(a) y = x + 3
(b) y = x + 7
(c) y = x - 7
(d) y = - x + 7

23. Determine which two equations represent perpendicular lines.
(a) y = 9x - 9 (b) y = x + 9
(c) y = - x + 9
(d) y = x - 9

24. Write the equation of the line that passes through point (0, -8) with a slope of .

25. Write the equation of the line passing through (6, 37) and (1, 12).

Attachments
Purchase this Solution
Solution Summary

Linear equations are investigated. The solution is detailed and well presented. The response received a rating of "5/5" from the student who originally posted the question.

Solution Preview

SOLUTIONS.

All the graphs were done by hand and are in the scanned document attached.

(1) Just substitute the numbers in to see if LHS (left hand side) = RHS (right hand side) and if they are equal then they are solutions!

(6,1): LHS = x + 2y = 6 + 2(1) = 8 = RHS yes
(8,0): LHS = x + 2y = 8 + 2(0) = 8 + 0 = 8 = RHS yes
(4,-2): LHS = x + 2y = 4 + 2(-2) = 4 + -4 = 0 NO (as it does not equal 8)
(-4,6): LHS = x + 2y = -4 + 2(6) = -4 +12 = 8 = RHS yes

So the three pairs (6,1), (8,0) and (-4,6) are solutions
and the pair (4,-2) is not a solution.
===================================================================================

(2) done by you already
====================================================================================
(3)

(5, ) : given x=5, find y. 2(5) + y = 10, so 10 + y = 10, so y=0. answer (5,0)
( ,10): given y=10, find x. 2x + 10 = 10, so 2x = 0, so x=0. answer (0,10)
( ,-2): given y=-2, find x. 2x + -2 = 10, so 2x = 10+2, so 2x = 12, so x=6. answer (6,-2)
(0, ) : given x=0, find y. 2(0) + y = 10, so y = 10 answer (0,10)

==========================================================================================

(4)

Just make up any four values for x and substitute into 3x+5y = 15, and solve for y.
Choose say x=0,1,2,3

When x=0, 3(0)+5y = 15, so 5y=15, so y=3 (0,3)
When x=1, 3(1)+5y = 15, so 3+5y=15, so 5y=12, so y=12/5=2.4 (1,2.4)
When x=2, 3(2)+5y = 15, so 6+5y=15,, so 5y=9 so y=9/5=1.8 (2,1.8)
When x=3, 3(3)+5y = 15, so 9+5y=15, so 5y=6, so y=6/5=1.2 ...

Purchase this Solution
Free BrainMass Quizzes
Know Your Linear Equations

Each question is a choice-summary multiple choice question that will present you with a linear equation and then make 4 statements about that equation. You must determine which of the 4 statements are true (if any) in regards to the equation.

Probability Quiz

Some questions on probability

Exponential Expressions

In this quiz, you will have a chance to practice basic terminology of exponential expressions and how to evaluate them.

Multiplying Complex Numbers

This is a short quiz to check your understanding of multiplication of complex numbers in rectangular form.

Geometry - Real Life Application Problems

Understanding of how geometry applies to in real-world contexts

View More Free Quizzes
Related BrainMass Solutions

  • methods of solving system of linear equation and inequality

    Solve systems of linear equations using the addition method 2. Solve applications of systems of linear equations The graphical method of solving equations, shown in Section 8.1, has two definite disadvantages.

  • Several problems on linear/quadratic equations

    199069 Several problems on linear/quadratic equations 1A: Applications of Linear Equations Solve the following questions and submit your response to the W4: Assignment 1 Dropbox. 1. Joe has a collection of nickels and dimes that is worth $5.65.

  • Real-Life Applications of Functions and Graphs : Heart Disease / Cancer and Fahrenheit / Celsius Temperature Conversions

    Using the equations of each line, make a reasonable prediction as to the number of deaths we might expect in 2005 due to each of these medical conditions. 2. a. Can the graphs that you constructed be classified as functions? Explain.

  • matrices and systems of linear equations

    A fourth-order linear equation can be solved by the 7. Solve these linear equations for x and y 8. The value of y in Question 7 is in the range 9. Which of the graphs in Fig. 38 is of f(x) = x^2 - 3x - 4? 10. Evaluate the determinant 11.

  • Comparing Graphs of Equalities and Inequalities

    You have already compared the graphs of linear equations with those of linear inequalities. Now you will make the same comparison with financial numbers.

  • Linear equations and inequalities

    Before you get started with the actual financial numbers, you will want to practice by creating and comparing various kinds of graphs. To start, you will be comparing the graphs of linear equations with those of linear inequalities.

  • Functions and Graphs

    A logarithmic function 3.Plot the graph of all the above equations. 4.Derive quadratic and linear equations from corresponding graphs. 1.Exponential Function : f(x) = 2x (refer Graph-1) Conversion to Logarithmic Function

  • Computer Applications and Substitution vs Elimination vs Matrix Methods

    Also, if we are dealing with problems in linear programming, where the equations are in the form of constraints (inequalities), it is always useful to graph the equations. Systems of Equations Computer Applications and Substitution vs.

  • Graphs

    170173 Graphs for Linear Algebra Equations I just need the graphs of the following equations. 1. y=1 2. y=x 3. y= x^2 4. y= 1/6(x^3) 5. y= 1/x^2 6. y= sin x 7. y = cos x 8. y = ln abs(x) 9. dy/dx = ½ x + 1 10. dy/dx = y 11. dy/dx = x-y 12

  • Questions about Linear Equations

    This answers some questions regarding equations, including real-life applications and how to interpret graphs.

View More Related Solutions