Warm Ups {(2,0) (-1,3) (2,4)} Write as table Write as graph Write as map State domain & range State the inverse

5-3 Equations as Relations Objective: To determine solutions to equations. Standard 16.0

Ordered pairs: always write in alphabetical order (x, y) (a, b) (r, s) Linear Equation: an equation that, when graphed, creates a straight line. Solution: ordered pairs that give a true statement

Example 1 Which of these are solutions of 3x + y = 8 ? Plug in the values for x and y Simplify each side Check if they are equal (4,-4) (8,0) (2,2) (3,1) x y 3(4) + (-4) = 8 12 + -4 = 8 8 = 8 Yes! x y 3(8) + 0 = 8 24 + 0 = 8 24 = 8 No! x y 3(2) + 2 = 8 6 + 2 = 8 8 = 8 Yes! x y 3(3) + 1 = 8 9 + 1 = 8 10 = 8 No!

Example 2 Solve the equation 2x + 2y = 14 given x = -3 2(-3) + 2y = 14 Substitute Solve for remaining variable Write as ordered pair 2x + 2y = 14 2(-3) + 2y = 14 -6 + 2y = 14 +6 +6 2y = 20 y = 10 (-3, 10)

Given the domain… Solve the equation x + y = 4 if the domain is {-4, -2, 0, 2, 4} Plug it in, domain = x Answer as ordered pairs!

What if… I gave you the range instead of the domain? How would you solve the equation given the range? Plug the values in for y, then solve for x

Example 3 Make a table and graph y = x + 6 if the domain is {-4,-3,2,4} This is a linear equation so you should be able to connect the dots and make a line. Answer: (-4,2) (-3,3) (2,8) (4,10)

TOO y = -1 for 3x = 13 – 2y x = 10 for 5x + 3 = y Answers (5, -1) (10, 53)

Homework 5-3 Practice

Math Lab Warm Ups {(3,-1) (0,4) (2,4) (3,3)} Write as table Write as graph Write as map State domain & range State the inverse

Practice 1 Solve the linear equation given the following domain: 2x+ y = 8 domain: {-2, -1, 0, 3, 6}

Practice 2 Solve the linear equation given the following range: 2x+ 4y = 10 range: {-1, 0, 1, 3, 6}