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Two variables show direct variation if their relationship can be written in the form y=ax, where a is the constant of variation. Direct variation equations represent relationships where one variable varies directly as the other changes. To determine if an equation represents direct variation, substitute coordinates to solve for the constant a and rewrite the equation in the form y=ax. The constant of variation and the graphs of direct variation equations can then be used to find output values for given input values.
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@ Business Mathematics Chapter 1& 2.pptx
This document provides an overview of the course "Business Mathematics" which covers topics like linear equations, nonlinear equations, and economic applications of linear and quadratic models. The course is targeted at second year ABVM students.
Unit one discusses linear equations, their basic concepts and properties. It also covers developing linear equations using the slope-intercept form, slope-point form, and two-point form. Nonlinear equations are defined as equations with terms of degree two or higher that do not represent straight lines.
Economic applications of linear and quadratic models are also discussed. Functions and curves are defined in economics, with examples like the relationship between money earned and hours worked given as a simple linear function.
11.1
This document provides examples of direct and inverse variation, including how to identify, graph, and write equations for direct and inverse variation relationships. It also contains examples of solving work problems using inverse variation.
Key points covered include:
- Direct variation is when y=kx and inverse variation is when y=k/x, where k is the constant of variation.
- Example 1 shows how to identify if an equation represents direct, inverse, or neither type of variation.
- Examples 2 and 3 demonstrate how to graph inverse variation equations.
- Examples 4, 5, and 6 show how to write inverse variation equations from tables of data or real-world context and solve problems using inverse variation equations.
linear equation in two variable.pptx
- The document discusses linear equations in two variables. It defines linear equations and explains that a linear equation in two variables can be written in the form ax + by = c.
- It describes how linear equations in two variables have infinitely many solutions, represented by pairs of x and y values. The graph of a linear equation in two variables is a straight line.
- The document also discusses how equations of lines parallel to the x-axis or y-axis can be represented. The graph of an equation of the form x = a is a line parallel to the y-axis, while an equation of the form y = a graphs as a line parallel to the x-axis.
Graphs linear equations and functions
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WRITING AND GRAPHING LINEAR EQUATIONS 1.pptx
The document discusses linear equations and graphing linear relationships. It defines key terms like slope, y-intercept, x-intercept, and provides examples of writing linear equations in slope-intercept form and point-slope form given certain information like a point and slope. It also discusses using tables and graphs to plot linear equations and find slopes from graphs or between two points. Real-world examples of linear relationships are provided as well.
identities1.2
The document discusses the concept of slope and how it is used to describe the steepness of a line. It defines slope as the ratio of the vertical change (rise) to the horizontal change (run) between two points on a line. Several forms of linear equations are presented, including point-slope form, slope-intercept form, and standard form. Relationships between parallel and perpendicular lines based on their slopes are also described. Examples are provided to demonstrate finding slopes, writing equations of lines, and determining if lines are parallel or perpendicular based on their slopes.
2.4 Writing Equations of Lines
The document provides instructions and examples for writing equations of lines using different methods such as given the slope and y-intercept, from a graph, using point-slope form, with two points, and for parallel and perpendicular lines. It also covers direct variation and writing linear models to predict data trends. Students are prompted to write equations or find values using the various line equation techniques covered.
9.1 inverse and joint variation
The document discusses different types of variation between variables:
- Direct variation means y = kx for some constant k.
- Inverse variation means xy = k for some constant k.
- To determine the type of variation, rewrite the equation by solving for y and check the pattern.
- Joint variation means z = kxy, where z varies directly with x and y.
4. Linear Equations in Two Variables 2.pdf
Math class 9 ppt is PPT Mein maine linear equation in two variable management
1539 graphs linear equations and functions
Mathematics (from Greek μάθημα máthēma, “knowledge, study, learning”) is the study of topics such as quantity (numbers), structure, space, and change. There is a range of views among mathematicians and philosophers as to the exact scope and definition of mathematics
Linear equations in Two Variable
The document discusses systems of linear equations and methods for solving them. It defines a system of linear equations as a pair of linear equations in two variables. It presents two examples of systems of linear equations. It then describes algebraic methods for solving systems, including elimination by substitution, elimination by equating coefficients, and cross multiplication. It provides examples of using elimination by substitution and elimination by equating coefficients to solve systems of two equations with two unknowns.
Direct variation-ppt
This document defines and provides examples of direct variation, also called direct proportion. It states that direct variation occurs when one quantity changes by the same factor as another quantity. The constant of proportionality or variation describes this fixed factor of change between the quantities. Examples are provided of direct variation situations in tables, equations, and graphs. The key characteristics of a direct variation graph are that it passes through the origin and yields increasing y-values as x increases. The document provides instructions for identifying and solving direct variation problems using tables, equations, and setting up proportions.
Maths
This document discusses linear equations in two variables. It defines linear equations in two variables as equations of the form ax + by = c, where a, b, and c are real numbers and a and b are not both zero. It explains that the graph of any linear equation in two variables is a straight line. It also categorizes different types of systems of linear equations based on the relationship between the lines: intersecting lines have a unique solution; coincident lines have an infinite number of solutions; and parallel lines have no solution. Methods for solving systems of linear equations like substitution, elimination, and graphing are also covered.
chapter1_part2.pdf
1. This document discusses linear equations, slope, graphing lines, writing equations in slope-intercept form, and solving systems of linear equations.
2. Key concepts explained include slope as rise over run, the different forms of writing a linear equation, finding the x- and y-intercepts, and using two points to write the equation of a line in slope-intercept form.
3. Examples are provided to demonstrate how to graph lines based on their equations in different forms, find intercepts, write equations from two points, and solve systems of linear equations.
Unit 4 hw 7 - direct variation & linear equation give 2 points
This document discusses direct variation, which is a linear equation that passes through the origin. It defines direct variation as y=kx, where k is the constant of variation. It provides examples of graphs that do and do not represent direct variations. It also shows step-by-step processes for finding the direct variation equation from two points, and for solving a direct variation problem when given a point and asked to find the corresponding y-value for a different x-value.
Directvariation
The document discusses direct variation, which is a relationship between two quantities where one quantity varies as the other changes such that they are proportional. It provides the definition of direct variation as y = kx, where k is the constant of variation. It gives examples of determining if an equation represents direct variation and writing an equation given a point. It also discusses using direct variation to find unknown values and illustrates direct variation through tables and graphs.
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4.6 notes
- 1. 4.6 Write and graph direct variation equations
- 2. Direct variation • Two variables x and y show direct variation provided y=ax and a does not equal zero. (y varies directly with x) • a is called the constant of variation – Example: y=5x • Any equation that can be rewritten as y=ax represents direct variation. – Example: 2x-3y=0
- 3. Determine whether each equation represents direct variation and identify the constant of variation: • -x+y=1 • 2x+y=0 • 4x-5y=0
- 4. Graphing direct variation equations
- 5. Graph direct variation equations xy 3 2 = y x
- 6. Graph direct variation equations xy 3−= y x
- 7. Identify the constant of variation • y=ax – Substitute coordinates – Solve for a – Rewrite equation • What is y if x is 3? • What is y if x is 600? y x (-2, 4)
Editor's Notes
- S=aw like y varies directly with x
- C=as – c is dependent on s – s is the input, c is the output. Dividing each cost by the number of songs results in a consistent amount (.99)