Section 2.2Graphing Linear Equations : Section 2.2Graphing Linear Equations Solutions of Equations in Two Variables
Graphing from a Table of Points
Graphing from the Intercepts
Horizontal & Vertical Lines
Linear Models
Solutions to Equations : Solutions to Equations A solution to an equation in two variables is any ordered pair of numbers (a,b) that makes a true statement when substituted into the equation.
Example: (2,7) is a solution to y = 3x + 1 because 7 = 3(2) + 1
You can find solutions by choosing a value for one variable, then solving the equation for the other variable
Example: For y = 3x + 1 Let x = 9 then y = 3(9) + 1 = 28 and this solution is shown by (9,28)
Class Exercise – Finding Solutions : Class Exercise – Finding Solutions a.) What is the solution when x = 6 ?
b.) What is the solution when y = 5 ?
Why graph equations? : Why graph equations? Consider the equation with two variables,
What will the solutions for this equation look like?
Ordered pairs: (x-value, y-value) (0,-3) for example
How many solutions are there?
Infinitely many
Definitions : Definitions The graph of an equation is the set of all points (x, y) on the rectangular coordinate system whose coordinates satisfy the equation. It is the visual solution set for the equation.
A linear equation in two variables is an equation that can be put into the form Ax+By=C (A and B can’t both be zero). The graph of a linear equation is always a line.
Rough Graphing : Rough Graphing Plan to use about 1/6 of a sheet of paper
Neatly draw the x-axis and y-axis
Label every 5 units -15 -10 -5 0 5 10 15 15 10 5 -5-10-15
Class Exercise – Graphing an Equation : Class Exercise – Graphing an Equation You already found two points: (6,3) and (0,5)
Find another point when x = -3
Use these 3 points to rough graph the equation
Graphing usingThe Intercept Method (“Cover-up Method”) : Graphing usingThe Intercept Method (“Cover-up Method”) The y-intercept of a line is the point (0, b), where the line intersects the y-axis.
To find b, substitute 0 for x in the equation of the line and solve for y.
The x-intercept of a line is the point (a, 0), where the line intersects the x-axis.
To find a, substitute 0 for y in the equation of the line and solve for x.
Another Example: 7x – 14y = 35
In-Class Exercises: : In-Class Exercises: Make a table of 3 points and use it to graph
Graph using intercepts:
How would you graph the following equations? : How would you graph the following equations?
Horizontal & Vertical Lines : Horizontal & Vertical Lines Is y = 3 a Linear Equation?
0x + y = 3 Yes! Is x = 2 a Linear Equation?
x + 0y = 2 Yes! Graph: x = -5 y=-4 y = 0
Horizontal and Vertical Lines : Horizontal and Vertical Lines If a is any real number: The graph of x = a is a vertical line with x-intercept (a, 0)
If a is 0, ( x = 0 ) the line is the y-axis.
If b is any real number: The graph of y = b is a horizontal line with y-intercept (0, b)
If b is 0, ( y = 0 ) the line is the x-axis.
Linear Models : Linear Models We can use linear equations to mathematically model some real-life situations. This way we can use observations about what happened in the past to predict what might take place in the future.
Exercise : Exercise 56. TELEPHONE COSTS In a community, the monthly cost of local telephone serviceis $5 per month, plus 25¢ per call.
a.Write a linear equation that gives the cost c for a. person making n calls.
b. Then graph the equation. (need 2 points)
c. Use the graph to estimate the cost of service in a month when 20 calls were made. c = 5 + .25n (0,?) -> (0,5)(10,?) -> (10,7.5)
What Next? : What Next? Present Section 2.3 Rate of Change & Slope of a Line
Accessing these Powerpoint Slides from the Internet:http://faculty.rcc.edu/vandewater/Section02_2.pptClick on Open