Example 1: Finding Solutions of Equations with Two Variables Use the given x-values to write solutions of the equation y = 4x + 2 as ordered pairs. x = 1, 2, 3, 4. Make a function table by using the given values for x to find values for y. Write these solutions as ordered pairs. (x, y)‏ 18 4(4) + 2 4 14 4(3) + 2 3 10 4(2) + 2 2 6 4(1) + 2 1 y 4x + 2 x (1, 6)‏ (2, 10)‏ (3, 14)‏ (4, 18)‏

Check It Out: Example 1 Use the given x-values to write solutions of the equation y = 3x + 2 as ordered pairs. x = 2, 3, 4, 5. Make a function table by using the given values for x to find values for y. Write these solutions as ordered pairs. 17 3(5) + 2 5 14 3(4) + 2 4 11 3(3) + 2 3 8 3(2) + 2 2 y 3x + 2 x (x, y)‏ (2, 8)‏ (3, 11)‏ (4, 14)‏ (5, 17)‏

Check if an ordered pair is a solution of an equation by putting the x and y values into the equation to see if they make it a true statement.

Additional Example 2: Checking Solutions of Equations with Two Variables Determine whether the ordered pair is a solution to the given equation. (3, 21); y = 7x Write the equation. y = 7x 21 = 7(3)‏ ? Substitute 3 for x and 21 for y. 21 = 21 ?  So (3, 21) is a solution to y = 7x.

Check It Out: Example 2 Determine whether the ordered pair is a solution to the given equation. (4, 20); y = 5x Write the equation. y = 5x 20 = 5(4)‏ ? Substitute 4 for x and 20 for y. 20 = 20 ?  So (4, 20) is a solution to y = 5x.

You can also graph the solutions of an equation on a coordinate plane You can also graph the solutions of an equation on a coordinate plane. When you graph the ordered pairs of some functions, they form a straight line. The equations that express these functions are called linear equations.

Additional Example 3: Reading Solutions on Graphs Use the graph of the linear function to find the value of y for the given value of x. x = 4 Start at the origin and move 4 units right. x y 4 Move up until you reach the graph. Move left to find the y-value on the y-axis. 2 -4 -2 0 2 4 -2 When x = 4, y = 2. The ordered pair is (4, 2). -4

Start at the origin and move 2 units right. Check It Out: Example 3 Use the graph of the linear function to find the value of y for the given value of x. x = 2 Start at the origin and move 2 units right. x y 4 Move up until you reach the graph. Move left to find the y-value on the y-axis. 2 -4 -2 0 2 4 -2 When x = 2, y = 4. The ordered pair is (2, 4). -4

Additional Example 4: Graphing Linear Functions Graph the function described by the equation. y = x + 2 Make a function table. Write these solutions as ordered pairs. 3 (1) + 2 1 2 (0) + 2 (–1) + 2 –1 y x + 2 x (x, y)‏ (–1, 1)‏ (0, 2)‏ (1, 3)‏

Additional Example 4 Continued Graph the ordered pairs on a coordinate plane. x y 5 4 Draw a line through the points to represent all the values of x you could have chosen and the corresponding values of y. 3 2 1 -5 -4 -3 -2 -1 0 1 2 3 4 5 -1 -2 -3 -4 -5

Check It Out: Example 4 Graph the function described by the equation. y = 2x-1 Make a function table. Write these solutions as ordered pairs. 1 2 (1) –1 –1 2 (0) –1 –5 2(-2) –1 –2 y 2x –1 x (x, y)‏ (–2, –5)‏ (0, –1)‏ (1, 1)‏

Check It Out: Example 4 Continued Graph the ordered pairs on a coordinate plane. x y 5 4 Draw a line through the points to represent all the values of x you could have chosen and the corresponding values of y. 3 2 1 -5 -4 -3 -2 -1 0 1 2 3 4 5 -1 -2 -3 -4 -5

An equation in function form: always starts with y = If an equation is written another way, you can rewrite it in function form Ex. 3x + y = 15 Subtract 3x from each side -3x -3x y = -3x + 15

Rewrite the equations in function form. -6x + y = 14 -3x - y = 24 -6x + 2y = 14 8x - 2y = 16