Lecture 07 graphing linear equations
- 1. Section 2.2 Graphing Linear Equations Solutions of Equations in Two Variables Graphing from a Table of Points Graphing from the Intercepts Horizontal & Vertical Lines Linear Models
- 2. 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)
- 3. Class Exercise – Finding Solutions 5 1 y x 3 a.) What is the solution when x = 6 ? b.) What is the solution when y = 5 ? 3 6 5 1 3 2 5 y y y 1 3 x x x 0 1 3 0 5 5 5 5
- 4. Why graph equations? Consider the equation with two variables, y 2x 3 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
- 5. 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.
- 6. 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 -15 -10 -5 0 5 10 15 -5 -10 -15
- 7. Class Exercise – Graphing an Equation 5 1 y x 3 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
- 8. Graphing using The Intercept Method (“Cover-up Method”) 1 y x 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 5 3
- 9. In-Class Exercises: Make a table of 3 points and use it to graph 5 2 1 y x 2 Graph using intercepts: 4x 3y 12
- 10. How would you graph the following equations? y 3 x 2
- 11. 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
- 12. 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.
- 13. 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.
- 14. Exercise 56. TELEPHONE COSTS In a community, the monthly cost of local telephone service is $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)
- 15. 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.ppt Click on Open