Complete the table of values for the linear function 3x+2y=−6.
Before completing the table of values, solve the given function in terms of ‘y’. This step is not necessary, but it does simplify the calculations.
3x+2y=−63x−3x+2y=−3x−6 2y=−3x−6 2y2=−3x2−62 y=−3x2−3
y=−3x2−3y=−3(−4)2−3y=−3x2−3y=−3(2)2−3y=122−3y=6−3y=3y=−62−3y=−3−3y=−6y=−3x2−3y=−3(0)2−3y=−3x2−3y=−3(6)2−3y=0−3y=−3y=−182−3y=−9−3y=−12
y=−32x−3
X Y
−4 3
0 −3
2 −6
6 −12
Example B
Use technology to create a table of values for the linear function f(x)=−12x+4.
When the table is set up, you choose the beginning number as well as the pattern for the numbers in the table. In this table, the beginning value for ‘x’ is –2 and the difference between each number is +2. The table is consecutive, even numbers. When consecutive numbers are used as the input numbers (x−values), there is a definite pattern in the output numbers (y−values). This will be expanded upon in a later lesson.
Example C
Complete the table of values for the following linear function, and use those values to graph the function.
x−2y=4x−x−2y=−x+4−2y=−x+4−2y−2=−x−2+4−2y=12x−2
y=12x−2 y=12(−4)−2 y=−2−2y=−4 y=12x−2 y=12(0)−2 y=0−2y=−2 y=12x−2 y=12(2)−2 y=1−2y=−1 y=12x−2 y=12(6)−2 y=3−2y=1
y=12x−2
X Y
−4 −4
0
Vocabulary
Linear Function
A linear function is a relation between two variables, usually x and y, in which each value of the independent variable (x) is mapped to one and only one value of the dependent variable (y).
Guided Practice
1. Complete the following table of values for the linear function 3x−2y=−12
3x−2y=−12
X Y
−6
−4
0
6
2. Use technology to complete a table of values for the linear function 2x−y=−8 and use the coordinates to draw the graph.
3. A local telephone company charges a monthly fee of $25.00 plus $0.09 per minute for calls within the United States. If Sam talks for 200 minutes in one month, calculate the cost of his telephone bill.
Answers
1. 3x−2y=−12 Solve the equation in terms of the variable ‘y’.
3x−3x−2y=−3x−12−2y=−3x−12−2y−2=−3x−2−12−2
y=32x+6 Substitute the given values for ‘x’ into the function.
y=32x+6 y=32(−6)+6 y=−9+6y=−3 y=32x+6 y=32(−4)+6 y=−6+6y=0 y=32x+6 y=32(0)+6 y=0+6y=6 y=32x+6 y=32(6)+6 y=9+6y=15
3x−2y=−12
X Y
−6 −3
−4 0
0 6
6 15
2. 2x−y=−8 To enter the function into the calculator, it must be in the form y=–––––––––––.
Solve the function in terms of the letter ‘y’.
2x−y=−8y=2x+82x−2x−y=−2x−8−y=−2x−8−y−1=−2x−1−8−1
The graph can also be done using technology. The table can be used to set the window.
3. y=0.09x+25 Write a linear function to represent the word problem.
yy=0.09(200)+25=$43.00Substitute the time of 200 minutes for the variable ‘x′.
The cost of Sam’s telephone bill is $43.00.
Summary
In this lesson, you have learned how to evaluate a linear function with given values. These values were given in table form. The table was completed by entering the values obtained from substituting the given values for ‘x’ into the linear function. These values were the coordinates of points that were located on the graph of the linear function. The points were used to draw the graph on a Cartesian plane.
The lesson then extended into the world of technology. The graphing calculator was used to create a table of values as well as to create the graph of the function. The more you practice the keystrokes for performing these tasks on the calculator, the more efficient you will become.
Problem Set
Solve each of the following linear functions in terms of the variable ‘y’.
2x−3y=18
4x−2y=10
3x−y=8
5x+3y=−12
3x−2y−2=0
For each of the following linear functions, create a table of values that contains four coordinates:
y=−4x+5
5x+3y=15
4x−3y=6
2x−2y+2=0
2x−3y=9
For each of the linear functions, complete the table of values and use the values to draw the graph.
y=−2x+1
x−3015y
x=2y−3
x−4026y
3x+2y=8
x−6−204y
4(y−1)=12x−7
x−2037y
12x+13y=6
x04610y
Using technology, create a table of values for each of the following linear functions. Using technology, graph each of the linear functions.
y=−2x+3
y=−12x−3
y=43x−2
Mr. Red is trying to estimate the cost of renting a car to go on vacation. He has contacted a rental agency and has obtained the following information. The agency charges a daily rate of $78.00 for the vehicle plus 45 cents per mile. If Mr. Red has $350 set aside for travel, create a table of values that will give him approximate distances that he can travel with this rental car.
Graphing a Linear Function Using the X- and Y-Intercepts
Objectives
The lesson objectives for Graphing a Linear Function Using the X- and Y-Intercepts are:
Understanding the x- and y−intercepts
Determining the x- and y−intercepts for a given linear function
Using the x- and y−intercepts to graph the linear function
this isnt my work but hopefully this helps i did the best i could given th info you gave me
