8.2 Equations W Two Variables

Chapter 8 Section 2: Equations with Two Variables. February 5 th , 2009

Warm Up ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

Two Variables ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

Example ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

Try These: Find y, and give Ordered Pair, x = -3 ,[object Object],[object Object],[object Object],y = -5, (-3, -5) y = -15, (-3, 15) y = -4, (-3, -4)

Real Life Example ,[object Object],t = 21 – 0.01(300) t = 21 – 3 t = 18 degrees Celsius The ordered pair solution for this equation is (300, 18). 300 is the domain, 18 is the range.

Try This One ,[object Object],[object Object],[object Object]

Graphing Equations with Two Variables. ,[object Object],[object Object],[object Object]

Graph: y = -0.5x + 3 ,[object Object],[object Object],(4, 1) y = -0.5(4) + 3, y = -2 + 3, y = 1 x = 4 (0, 3) y = -0.5(0) + 3, y = 0 + 3, y = 3 x = 0 (-2, 4) y = -0.5(-2) + 3, y = 1 + 3, y = 4 x = -2 Ordered Pairs (x, y) Equation: y = -0.5x + 3 Values for X (that we make up)

Graph These For Me In Your Notes, The Connect The Dots ,[object Object],[object Object],Pick reasonable numbers for x so that you can solve for y and find the ordered pair that allows you to graph the equation. You need three points to graph so that you know you have done it correctly.

Linear Equations and Vertical Line Test ,[object Object],[object Object],[object Object],[object Object]

Graph These Equations ,[object Object],[object Object],For every value of x, y ALWAYS equals 2. No matter what. For every value of y, x ALWAYS equals 2. No matter what. This is the graph for y = 2, it is a horizontal line. Does it pass the vertical line test? This is the graph for x = 2, it is a vertical line. Does it pass the vertical line test? Yes! Y = 2 is a function! No! X = 2 is NOT a function!

One More Example ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],(x, y) -3x – 5 X

Solve each equation for y, then graph. ,[object Object],[object Object],[object Object],[object Object]

Assignment #2 ,[object Object],[object Object],[object Object]

8.2 Equations W Two Variables

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8.2 Equations W Two Variables