Name: Period: Date: Algebra I
嚜燒ame: ____________________________ 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 = 每 (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 = 每3
2. x + 5y = 每10
Graph each equation using x- and y-intercepts.
3. 3x + y = 每2
4. 2x 每 3y = 每 6
For the equation, tell whether its graph is a horizontal or a vertical line.
5. x = 每1
Standard Form
Graph the equation.
6. x = 每5
7. Writing Explain how y 每 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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