4.2 – GRAPHING LINEAR EQUATIONS

ALGEBRA 1(A/B)

FALL 2012

WARM-UPSolve 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 = -10 y = 16

4.2 – GRAPHING LINEAR EQUATIONS

OBJECTIVES• Graph a using a table.

• Graph and lines.

linear equation

horizontal vertical

SOLUTION OF AN EQUATIONIt 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

pointsequation

How many solutions did we have in our previous example?

HOW TO CHECK IF A POINT IS A SOLUTIONMethod 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

Yes

No

HOW TO CHECK IF A POINT IS A SOLUTIONMethod 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

Yes

No

BREAK TIME

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

Iron curtain Breakfast Leftovers

USING A TABLE TO GRAPH AN EQUATIONSteps:

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 – 1Step 1: Rewrite the equation so that it says “y = …”

USE A TABLE TO GRAPH THE FOLLOWING EQUATION

y = 2x – 1Step 2: Make a table and choose values for x.

x y

USE A TABLE TO GRAPH THE FOLLOWING EQUATION

y = 2x – 1Step 3: Plot the points on a coordinate plane and graph with a straight line.

x y

PAIRS PRACTICEGraph y + 2 = 3x.

PAIRS PRACTICEGraph y + 3 = x.

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

GRAPHING HORIZONTAL AND VERTICAL LINESHorizontal = 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. 214-215 #12-20 even, 30, 31, 36-38