5-5 STANDARD FORM

Today, we will use to graph a line.

The is the x-coordinate of a point where a graph crosses the x-axis. The y-intercept occurs when the value of is zero. The x-intercept occurs when the value of is zero.

Standard Form of a Linear Equation: _____________ where A, B, and C are , A is positive and A and B are not both zero.

When an equation is written in Standard Form it is easy to graph using the intercepts.

INTERCEPTS

x-INTERCEPT

xy

Ax By C REAL NUMBERS

Find the intercepts of the following graphs of the equation:

1) To find the x-intercept, substitute 0 in for y. Solve for x.    2) To find the y-intercept, substitute 0 in for x. Solve for y.

FINDING INTERCEPTS7x y

The x-intercept is 77x y

0 7x 7x

7x y 0 7y

7y

The y-intercept is 7

GRAPHING USING INTERCEPTSWhat is the graph of ? 1) x- intercept:   2) y- intercept:  

3) Plot the points 4) Draw a line through the points.  

4 3(0) 12x

4 3 12x y

4 12x 3x

3

4y 3 12y

4(0) 3 12y 4

(3,0) (0, 4)

HORIZONTAL AND VERTICAL LINESThe graph of is a horizontal line, and the graph of is a vertical line, where a and b are constants.

Given the equation graph the line: Rewrite in Standard Form: Name two points on the line:

Given the equation graph the line: Rewrite in Standard Form: Name two points on the line:

1x

0 1 4x y (0,4) (4,4)

4y

y b x a

( 1,0) ( 1,5)1 0 1x y

For all values of y, x = -1

For all values of x, y = 4

TRANSFORMING AN EQUATION TO STANDARD FORMWhat is written in standard form using integers?

1) Clear the fractions. 

2) Rewrite so that the x and y values are on the same side of the equation:  3) Make the value of x positive:

34

5y x

35 4

5y x

5 3 20y x

3 5 20x y

1 3 5 20x y

3 5 20x y

TRANSFORMING AN EQUATION TO STANDARD FORMWhat is written in standard form using integers?

1) Use Distributive Property.

2) Rewrite so that the x and y values are on the same side of the equation:  3) Move the constants to the right side of the equation:

6 3( 1)y x

3 6 3x y

3 9x y

6 3 3y x

A festival sells ride tickets for $0.50 each and game tickets for $0.20 each. You have $5 to spend on tickets at the festival. Define variables: Equation:  If you buy no game tickets how many ride tickets can you get? If you buy no ride tickets how many game tickets can you get? Find another combination:

USING STANDARD FORM AS A MODEL

ride

5

10

2 4 106

25x = ride ticketsy = game tickets

.5 .2 5x y 5 2 50x y

game

10x

25y

15

20

8

(8,5) (6,10) (4,15)

HOMEWORK: P. 354-355 #’S 8-34 EVEN

TRY THESEFind the intercepts of the following graphs of the equations:1)

2)    

4 2 8x y 3 4 12x y 4 2(0) 8x

4 8x

2x

4y

2 8y 4(0) 2 8y

3 4(0) 12x

3 12x

4x

3(0) 4 12y 4 12y

3y

TRY THESE

Tell which form each linear equation is in:

1.

2.

3.

4.

5 ( 2)y x

2 5y x

10 2( 1)y x

2 4 12x y

Point-slope form

Point-slope form

Slope-intercept form

Standard form