Download STATION #1: Writing Equations in FUNCTION FORM Example: Write

STATION #1: Writing Equations in FUNCTION FORM
…in other words, get y all by itself on one side
of the equal sign!!!
Example: Write 9𝑥 − 4𝑦 = 8 in function form
9𝑥 − 4𝑦 = 8
Write original equation
9𝑥 − 4𝑦 = 8
−9𝑥
−9𝑥
First isolate the term containing 𝑦
−4𝑦 = 8 − 9𝑥
Subtract 9𝑥 from both sides
−4𝑦 = 8 − 9𝑥
Now get 𝑦 all by itself
−4
−4
−4
9
𝑦 = −2 + 𝑥
4
Divide both sides by −4
9
The equation 𝑦 = −2 + 𝑥 is in function form!!
4
STATION #2: Graphing using a TABLE OF VALUES
Example: Graph the equation 3𝑦 = 6𝑥 − 3.
STEP 1:
Solve the equation for y
3𝑦 = 6𝑥 − 3
𝑦 = 2𝑥 − 1
STEP 2:
x
-2
-1
0
1
2
(divide both sides by 3)
Make a table of values by choosing 5 values for x (2 positive,
2 negative, and zero). Find the values of y for each of these
x-values.
y
Example for 𝑥 = −2
𝑦 = 2(−2) − 1
𝑦 = −4 − 1
𝑦 = −5
x
-2
-1
0
1
2
y
-5
-3
-1
1
3
STEP 3:
Plot the points. Notice that the points appear to lie on a
line.
STEP 4:
Connect the points
by drawing a line through
them. Use arrows to
indicate that the graph
goes on without end.
2
2
STATION #3: Graphing using INTERCEPTS
Example: Graph 2𝑥 − 4𝑦 = 16 using intercepts.
STEP 1:
Find the x-intercept: Substitute y = 0 and solve for x
2𝑥 − 4(0) = 16
2𝑥 = 16
𝑥=8
STEP 2:
The graph crosses the x-axis at (8, 0).
Find the y-intercept: Substitute x = 0 and solve for y
2(0) − 4𝑦 = 16
−4𝑦 = 16
𝑦 = −4
The graph crosses the y-axis at (0, −4).
STEP 3:
Plot & Label the two ordered
pairs from Step 1 and Step 2
STEP 4:
Connect the points
by drawing a line through
them. Use arrows to
indicate that the graph
goes on without end.
2
2
(0, -4)
(8, 0)
STATION #4: HORIZONTAL & VERTICAL LINES
Horizontal Lines: Equations of horizontal lines only have a y-variable
Example: y = -5
Remember: The equal sign (=),
represents the word “is” in a
sentence.
(0, -5)
So the equation y = -5
can be thought of as
“everywhere y is -5”
Consider the table
of values for y = -5:
x
4
-2
3
-9
10
y
-5
-5
-5
-5
-5
y is always -5!!
It doesn’t matter what value you
choose for x
Vertical Lines: Equations of horizontal lines only have a x-variable
Example: x = 4
The equation x = 4
can be thought of as
“everywhere x is 4”
(4, 0)
Consider the table
of values for x = 4:
x
4
4
4
4
4
y
-5
2
-12
34
5
x is always 4!!
It doesn’t matter what value you choose for y!!
STATION #5: Finding SLOPE
Example 1:
Recall:
The slope of a line rising from left to right will be positive.
The slope of a line falling from left to right will be negative.
Example 2:
Recall:
The slope of all horizontal lines will be zero.
The slope of all vertical lines will be undefined.
STATION #6: Graph using SLOPE-INTERCEPT FORM
Example:
STATION #7: REVIEW
Example 1:
Example 2: