Name: Period: Date: Algebra I

Name: ____________________________ Period: ______ Date: __________ Algebra I

Notes for 5.5 Standard Form

What you¡¯ll learn: To graph linear equations using intercepts. To write linear equations in standard form.

Vocabulary: x-intercept, standard form of a linear equation

Standard Form of a Linear Equation: The standard form of a linear equation is Ax+By=C where A,B,and C

are real numbers and A and B are not both zero. For example: 4x+2y=13 and 5x-2y=-6

Write each equation in standard form using integers.

a). y + 5 = ¨C (x + 3)

b). y = ?

Finding the x and y intercept

What are the x and the y intercepts of the graph 3x+4y=24

X-intercept

Step 1: set y = 0

Y-intercept

Step2: set x = 0

2

3

x+6

Your turn: What are the x and y intercept of the graph of each equation? Graph after.

c) 5x-6y=60

d) 3x+8y=12

Take a note: If A=0 in the standard form Ax+By=C then you can write the equation in the form y=b, where b is

a constant and the graph will be a horizontal line.If B=0 in the standard form Ax+By=C then you can write the

equation in the form x=a, where a is a constant and the graph is a vertical line.

Your turn

What is the graph of each equation? Write them in the standard form

A. x=3

B. y=3

C. x=4

D. x=-5

E. y=0

Using the Standard Form as a Model

A media download store sells songs for $1 each and movies for $12 each. You have $60 to spend. Write and

graph an equation that describes the items you purchase. What are three combinations of numbers of songs and

movies you can purchase?

Your turn

a) Can you buy half of a song or a movie?

b) Suppose the store charged $15 for each movie. What equation describes the numbers of songs and movies

you can purchase for $60?

c) What domain and range are reasonable for the equation in part b). Explain

Take a note:

Slope intercept form

Point Slope Form

Section (5.5)

CLASSWORK

Find the x- and y-intercepts of the graph of each equation

1. x + y = ¨C3

2. x + 5y = ¨C10

Graph each equation using x- and y-intercepts.

3. 3x + y = ¨C2

4. 2x ¨C 3y = ¨C 6

For the equation, tell whether its graph is a horizontal or a vertical line.

5. x = ¨C1

Standard Form

Graph the equation.

6. x = ¨C5

7. Writing Explain how y ¨C 2 = 2(x + 6) can be rewritten into standard form. Then show

your work in transforming the equation to standard form.

8. Mike was the kicker for the football team. He scored 56 points during the season kicking

field goals (3 points) and extra points (1 point). Write and graph an equation that represents

this situation. What are three combinations of field goals x and extra points y he could have

made?

For each graph, find the x- and y-intercepts. Then write an equation in standard form using integers.

9.

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