Problem 1) A cab company charges a $3 boarding rate in addition to its meter which is $2 for every mile. What is the equation of the line that represents this cab company's rate? |

Problem 2) A cab company charges a $5 boarding rate in addition to its meter which is $3 for every mile. What is the equation of the line that represents this cab company's rate? |
Slope of this line : 3
y-intercept of line: 5
Equation of this line(slope intercept form) : y = 3x +5

Problem 3) A cab company charges a $3 boarding rate in addition to its meter which is $½ for every mile. What is the equation of the line that represents this cab company's rate? |
Slope of this line : ½
y-intercept of line: 3
Equation of this line(slope intercept form) : y = ½x +3

Problem 4) A cab company charges a $4 boarding rate in addition to its meter which is $ ¾ for every mile. What is the equation of the line that represents this cab company's rate? |
Slope of this line : ¾
y-intercept of line: 4
Equation of this line(slope intercept form) : y = ¾x + 4

Problem 5) A cab company does not charge a boarding fee but then has a meter of $4 an hour.What equation represents this cab company's rate? |
Slope of this line : 4
y-intercept of line: 0
Equation of this line(slope intercept form) : y = 4x

Problem 6) A cab company does not charge a boarding fee but then has a meter of $4 an hour.What equation represents this cab company's rate? |
Slope of this line : 4
y-intercept of line: 0
Equation of this line(slope intercept form) : y = 4x

Problem7) A cab company charges a $1 boarding fee and has a meter of $1/3 an hour.What equation represents this cab company's rate? |
Slope of this line : 1/3
y-intercept of line: 1
Equation of this line(slope intercept form) : y = 1/3x+1

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| At how many mnutes do both companies charge the same amount? | Never, the slope of the graphs of...

...2014/9/16
LinearEquations
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LinearEquations
A linearequation is an equation for a straight line
These are all linearequations:
y = 2x+1
5x = 6+3y
y/2 = 3 x
Let us look more closely at one example:
Example: y = 2x+1 is a linearequation:
The graph of y = 2x+1 is a straight line
When x increases, y increases twice as fast, hence 2x
When x is 0, y is already 1. Hence +1 is also needed
So: y = 2x + 1
Here are some example values:
http://www.mathsisfun.com/algebra/linear-equations.html
x
y = 2x + 1
1
y = 2 × (1) + 1 = 1
0
y = 2 × 0 + 1 = 1
1
y = 2 × 1 + 1 = 3
1/6
2014/9/16
LinearEquations
2
y = 2 × 2 + 1 = 5
Check for yourself that those points are part of the line above!
Different Forms
There are many ways of writing linearequations, but they usually have constants (like "2" or
"c") and must have simple variables (like "x" or "y").
Examples: These are linearequations:
y = 3x 6
y 2 = 3(x + 1)
y + 2x 2 = 0
5x = 6
y/2 = 3
But the variables (like "x" or "y") in LinearEquations do NOT have:
Exponents (like the 2 in x2)
Square roots, cube roots, etc
Examples: These are NOT linearequations:
...

...Algebra I Chapter 5 Study Guide Writing LinearEquations
Name ________________
Due: Tuesday, January 17 (Exam week)
100 points
Writing LinearEquations in a Variety of Forms
Using given information about a __________, you can write an ________________of the line in _____________ different forms. Complete the chart:
Form (Name)
Equation
• •
Important information
The slope of the line is ____. The __ - ___________ of the line is _____. The slope of the line is _____. The line passes through ( ______, ______ ) A, B, and C are __________ numbers. A and B are not both ___________.
Slope – Intercept
Point – Slope
• •
Standard
• •
Try a few (Page 345 – 347) Write an equation in Slope – Intercept Form:
Algebra I
Study Guide Chapter 5
lopeWrite an equation in Slope-Intercept Form that passes through the given point and has the given slope m.
8. (23, 21); m = 4 y= m= x= b= 9) (– 2, 1), m = 1 y= m= x= b= 10) (8, –4) m = – 3 y= m= x= b=
Write an equation in Point-Slope Form that passes through the given points. oint11) (4, 7) (5, 1) 12) (9, 22) (23, 2) 13) (8, 28) (23, 22)
(Hint: you need slope)
(Hint: you need slope)
(Hint: you need slope)
-2-
Algebra I
Study Guide Chapter 5
Write an equation in Standard Form of the line that has the given characteristics.
Hint for #15 & #16 You’ll...

...Patterns within systems of LinearEquations
HL Type 1 Maths Coursework
Maryam Allana
12 Brook
The aim of my report is to discover and examine the patterns found within the constants of the linearequations supplied. After acquiring the patterns I will solve the equations and graph the solutions to establish my analysis. Said analysis will further be reiterated through the creation of numerous similar systems, with certain patterns, which will aid in finding a conjecture. The hypothesis will be proven through the use of a common formula. (This outline will be used to solve both, Part A and B of the coursework)
Part A:
Equation 1: x+2y= 3
Equation 2: 2x-y=4
Equation 1 consists of three constants; 1, 2 and 3. These constants follow an arithmetic progression with the first term as well as the common difference both equaling to one. Another pattern present within Equation 1 is the linear formation. This can be seen as the equation is able to transformed into the formula ‘y = mx+c’ as it is able to form a straight line equation (shown below). Similar to Equation 1, Equation 2 also follows an arithmetic progression with constants of; 2, -1 and 4. It consists of a starting term of 2 and common difference of -3. As with Equation 1,...

...Summer 2010-3 CLASS NOTES CHAPTER 1
Section 1.1: LinearEquations
Learning Objectives:
1. Solve a linearequation
2. Solve equations that lead to linearequations
3. Solve applied problems involving linearequations
Examples:
1. [pic]
[pic]
3. A total of $51,000 is to be invested, some in bonds and some in certificates of deposit (CDs). If the amount invested in bonds is to exceed that in CDs by $3,000, how much will be invested in each type of investment?
4. Shannon, who is paid time-and-a-half for hours worked in excess of 40 hours, had gross weekly wages of $608 for 56 hours worked. What is her regular hourly wage?
Answers: 1. [pic]
2. [pic]
3. $24,000 in CDs, $27,000 in bonds 4. $9.50/hour
Section 1.2: Quadratic Equations
Learning Objectives:
1. Solve a quadratic equation by (a) factoring, (b) completing the square, (c) the
quadratic formula
2. Solve applied problems involving quadratic equations
Examples:
1. Find the real solutions by factoring: [pic]
2. Find the real solutions by using the square root method: [pic]
3. Find the real solutions by completing the square: [pic]
4. Find the real solutions...

...other than lowering a high school student's grade point average. Systems of linearequations, or a set of equations with two or more variables, are an essential part of finding solutions with only limited information, which happens to be exactly what algebra is. As a required part of any algebra student's life, it is best to understand how they work, not only so an acceptable grade is received, but also so one day the systems can be used to actually find desired information with ease.
There are three main methods of defining a system of linearequations. One way is called a consistent, independent solution. This essentially means that the system has one unique, definite solution. In this situation on a graph, a set of two equations and two variables would be solved as one single point where two lines intersect. It is much the same with three variables and three equations. The only difference is that the point is an intersection of three planes instead of two lines.
Additionally, there are situations where a system of linearequations could be described as consistent, dependent. These systems of linearequations have an infinite number of solutions where a general solution is used to substitute one or two variables for one other selected variable, and solves the other unknown variable or variables in terms of that...

...Weeks One and Two
Chapter 4 Systems of LinearEquations; Matrices (Section 4-1 to 4-6) | Examples | Reference (Where is it in the text?) |
| | |
DEFINITION: Systems of Two LinearEquations in Two VariablesGiven the linear system ax + by = hcx + dy = kwhere a , b , c , d , h , and k are real constants, a pair of numbers x = x0 and y = y0 [also written as an ordered pair (x0, y0)] is a solution of this system if each equation is satisfied by the pair. The set of all such ordered pairs is called the solution set for the system. To solve a system is to find its solution set. | EXAMPLE 1 Solving a System by Graphing Solve the ticket problem by graphing2x + y = 8x + 3 y = 9SOLUTION An easy way to find two distinct points on the first line is to find the x and y intercepts.Substitute y = 0 to find the x intercept (2x = 8, so x = 4), and substitute x =0 to find the y intercept (y = 8).Then draw the line through (4, 0) and (0, 8).After graphing both lines in the same coordinate system (Fig. 1), estimate the coordinates of the intersection point: | Page 170 |
Systems of LinearEquations: Basic TermsDefinition: A system of linearequations is consistent if it has one or more solutions andInconsistent if no solutions exist. Furthermore, a consistent system is said to be independent if it has exactly one solution...

...MODULE - 1
LinearEquations
Algebra
5
Notes
LINEAREQUATIONS
You have learnt about basic concept of a variable and a constant. You have also learnt
about algebraic exprssions, polynomials and their zeroes. We come across many situations
such as six added to twice a number is 20. To find the number, we have to assume the
number as x and formulate a relationship through which we can find the number. We shall
see that the formulation of such expression leads to an equation involving variables and
constants. In this lesson, you will study about linearequations in one and two variables.
You will learn how to formulate linearequations in one variable and solve them algebraically.
You will also learn to solve linearequations in two variables using graphical as well as
algebraic methods.
OBJECTIVES
After studying this lesson, you will be able to
•
identify linearequations from a given collection of equations;
•
cite examples of linearequations;
•
write a linearequation in one variable and also give its solution;
•
cite examples and write linearequations in two variables;
•
draw graph of a linearequation in two...

...1 ) The sum of the digits of a two-digit number is 7. When the digits are reversed, the number is increased by 27. Find the number.
2 ) A passenger jet took three hours to fly 1800 miles in the direction of the jetstream. The return trip against the jetstream took four hours. What was the jet's speed in still air and the jetstream's speed?
3 ) These circles are identical. What is the value of x ?
4 ) Solve for x using these two equations: 2x + 6 = y; y - x = 2
5 ) The perimeter and the area of this shape are equal. What is the value of x?
6) Shobo’s mother’s present age is six times Shobo’s present age . Shobo’s age five years from now will be one third of his mother’s present age . What are their present ages ?
7)There is a narrow rectangular plot , reserved for a school in A Mahuli village . The length and breadth of the plot are in the ratio 11:4 . At the rate of Rs. 100 per meter it will cost the village panchayat Rs. 75000 to fence the plot . What rare the dimensions of the plot ?
8)Solve the following equations and check your results :
1 . 3x = 2x + 18
2 . 5t-3 = 3t-5
3 . 5x + 9 = 5 = 3x
4 . 4z = 3 = 6 = 2x
5 . 2x- 1 = 14 – x
9 )The organizers of an essay competition decide that a winner in the competition gets a prize of Rs. 100 and a participant who does not win get a prize of Rs. 25 . The total prize money distributed is Rs . 3000 . Find the number of winners , if the total number of participants...

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