Download graphing linear equations

Graphing Linear Equations
Objectives:
…to check and find possible solutions to equations with two variables
...to graph solutions to linear equations on the coordinate plane
Assessment Anchor:
8.C.3.1 – Plot and/or identify ordered pairs on a coordinate plane.
8.D.4.1 – Represent relationships with tables or graphs on the coordinate
plane.
NOTES (checking)
To check if an ordered pair is a solution to an equation containing two
variables (x and y):
1. Substitute the “x” and “y” values into the equation for “x” and “y”
respectively
2. Simplify each side of the equation as far as possible
3. Determine if the numerical statement is TRUE or FALSE. If it is
TRUE, then the ordered pair is a solution.
EXAMPLES
1a) Is the ordered pair (2, 1) a solution to:
Substitute
(2, 1) IS a solution!
1b) Is the ordered pair (-1, 3) a solution to:
Substitute
(-1, 3) is NOT a solution!
4x + 2y = 10
4(2) + 2(1) = 10
8 + 2 = 10
10 = 10 TRUE!
4x + 2y = 10
4(-1) + 2(3) = 10
-4 + 6 = 10
2 = 10 FALSE!
Graphing Linear Equations
1c) Is the ordered pair (5, -5) a solution to:
4x + 2y = 10
Substitute
2a) Is the ordered pair (-4, -1) a solution to:
Substitute
(-4, -1) is NOT a solution!
2b) Is the ordered pair (1, -3) a solution to:
-2y = 5x – 11
-2(-1) = 5(-4) – 11
2 = -20 – 11
2 = -31 FALSE
-2y = 5x – 11
Substitute
“Remember, there are an infinite number of
ordered pairs that will be solutions to
an equation with two variables.”
MORE NOTES (finding)
To find a solution to an equation containing two variables (x and y):
1. Choose a value for “x”. You may choose any number you wish.
2. Substitute that value into the equation for “x”, and solve for “y”
3. Write your solution as an ordered pair (x,y)
Graphing Linear Equations
EXAMPLES
3)
4)
Find 3 solutions to:
4x + 2y = 10
1st solution
2nd solution
3rd solution
Choose… x = 3
Choose… x = -5
Choose… x = 6
4x + 2y = 10
4(3) + 2y = 10
12 + 2y = 10
– 12
– 12
2y = -2
2 2
y = -1
4x + 2y = 10
4(-5) + 2y = 10
-20 + 2y = 10
+ 20
+ 20
2y = 30
2 2
y = 15
4x + 2y = 10
4(6) + 2y = 10
24 + 2y = 10
– 24
– 24
2y = -14
2
2
y = -7
1st solution: (3, -1)
2nd solution: (-5, 15)
3rd solution: (6, -7)
Find 3 solutions to:
3y = 8x + 1
1st solution
2nd solution
3rd solution
Choose…
Choose…
Choose…
Graphing Linear Equations
Vocabulary alert!!
LINEAR EQUATION – an equation whose graph is a
straight line
EVEN MORE NOTES (graphing)
To graph linear equations (using T-tables):
1. Make a T-table that contains at least 3 ordered pairs
a. Choose whatever numbers you want for “x”, but keep it simple
b. Substitute a value for “x”, solve for “y” and fill in the table
2. Make the graph
a. The straight line shows all possible solutions to the equation
b. If points don’t make straight line, double check the
calculations in step #1 and the plotting of ordered pairs
c. Don’t forget to include arrows on your line!
COORDINATE PLANE
y-axis
Quadrant II
Quadrant I
Quadrant III
Quadrant IV
x-axis
origin
Graphing Linear Equations
EXAMPLES
5)
Graph this equation:
y = 3x – 2
T-Table
Use x = 1
x
0
1
2
y
-2
1
4
y = 3(1) – 2
y=3–2
y=1
Use x = 0
Use x = 2
y = 3(0) – 2
y=0–2
y = -2
y = 3(2) – 2
y=6–2
y=4
6)
Graph this equation:
Solve for “y” first:
4y = -8x + 20
4
4
y = -2x + 5
T-Table
Use x = 1
x
0
1
2
y
5
3
1
y = -2(1) + 5
y = -2 + 5
y=3
Use x = 0
Use x = 2
y = -2(0) + 5
y=0+5
y=5
y = -2(2) + 5
y = -4 + 5
y=1
4y = -8x + 20
Now graph: y = -2x + 5
Graphing Linear Equations
7)
Graph this equation:
y= x+4
Graph this equation:
2y – 8 = -6x
T-Table
x y
8)
Solve for “y” first:
T-Table
x y