4.2 – GRAPHING LINEAR EQUATIONS ALGEBRA 1(A/B) FALL 2012

WARM-UP Solve each equation for y. 1)2x + y = 10 2) 6x – 3y = -3 Find the value of y when x = -3. 3)y = x – 7 4) y = -5x + 1 y = -2x + 10 y = 2x + 1 y = -10y = 16

4.2 – GRAPHING LINEAR EQUATIONS OBJECTIVES Graph a using a table. Graph and lines. linear equation horizontalvertical

SOLUTION OF AN EQUATION It is an ordered pair (x, y) that makes an equation true. Example: x + 3y = 6 Is (1, 2) a solution? Is (-3, 3) a solution?

IS (-3, 3) THE ONLY SOLUTION? x + 3y = 6 In your pairs, try to come up with other solutions to the equation! Try to come up with at least 2 more solutions.

x + 3y = 6 SOLUTIONS OF THE EQUATION Solutions: What would it look like if we plotted the solutions of the equation on a coordinate plane?

All the that lie on the line are the solutions to the ! SOLUTIONS TO A LINEAR EQUATION points equation How many solutions did we have in our previous example?

HOW TO CHECK IF A POINT IS A SOLUTION Method 1: Using a Graph Check to see if the point is on the line. Is (3, 1) a solution of the equation 2x – y = 5? Is (0, -4) a solution of the equation 2x – y = 5? Is (5, 5) a solution of the equation 2x – y = 5? Yes No

HOW TO CHECK IF A POINT IS A SOLUTION Method 2: Checking algebraically Plug the point into the equation and see if it is true. Is (3, 1) a solution of the equation 2x – y = 5? Is (0, -4) a solution of the equation 2x – y = 5? Is (5, 5) a solution of the equation 2x – y = 5? Yes No

BREAK TIME Use this time to relax, stretch out, talk to a neighbor, or try the following rebus puzzles. Iron curtainBreakfastLeftovers

USING A TABLE TO GRAPH AN EQUATION Steps: 1.Rewrite the equation so that it says “y = …” – (called function form) 2.Make a table and choose values for x. 3.Plot the points on a coordinate plane and graph with a straight line.

USE A TABLE TO GRAPH THE FOLLOWING EQUATION y = 2x – 1 Step 1: Rewrite the equation so that it says “y = …”

USE A TABLE TO GRAPH THE FOLLOWING EQUATION y = 2x – 1 Step 2: Make a table and choose values for x. xy

USE A TABLE TO GRAPH THE FOLLOWING EQUATION y = 2x – 1 Step 3: Plot the points on a coordinate plane and graph with a straight line. xy

PAIRS PRACTICE Graph y + 2 = 3x.

PAIRS PRACTICE Graph y + 3 = x.

PAIRS PRACTICE (CHALLENGE) Graph 3y + 3 = 6x.

GRAPHING HORIZONTAL AND VERTICAL LINES Horizontal = left to right Vertical = up and down x = any number y = any number MEMORIZE THIS! vertical line horizontal line

HORIZONTAL LINES

GRAPH THE FOLLOWING EQUATION y = 5 Horizontal line where every y-coordinate on the line is 5.

GRAPH THE FOLLOWING EQUATION y = -1

VERTICAL LINES

GRAPH THE FOLLOWING EQUATION x = -3 Vertical line where every x-coordinate on the line is -3.

GRAPH THE FOLLOWING EQUATION x = 5

EXTRA PRACTICE Is the point (1, 3) a solution to the equation 4x – y = 1?

EXTRA PRACTICE Rewrite the following equation by solving for y. 6x – 3y = 12

EXTRA PRACTICE Make a table and graph. y = 2x - 4

EXTRA PRACTICE Does the point (-1, 2) lie on the graph of the line 3x – 4y = 10?

EXIT SLIP Clear your desks! When you are done with your exit slip, begin working on the homework assignment! Homework: pgs #12-20 even, 30, 31, 36-38