ch 4.2 objective: to graph linear equations. definitions linear equation an equation containing two...
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Ch 4.2
Objective:
To graph linear equations
DefinitionsLinear Equation
An equation containing two variables that when points are plotted create a line.
Generally of the form: ax + by = c
where (x,y) are coordinates and a, b, and c are numbers.
Steps for graphing1) Choose a value for “x”.
2) Plug that value into the equation and solve for “y”.
3) Plot the coordinate (x,y).
4) Choose another value for “x”
5) Plug that value into the equation and solve for “y”
6) Plot the coordinate (x,y).
7) Draw a line through the two points.
1
2
4
5
7
2 2
Comparison
One Variable Equations Two Variable Equations
2x - 3 = 11+3 +3
2x = 14
x = 7
One Solution
x + y = 5
Solutions:x = 1, y = 4
x = 2, y = 3
x = 4, y = 1
x = 5, y = 0
x = 7, y = -2
OrderedPairs (x,y)
(1,4)
(2,3)
(4,1)
(5,0)
(7,-2)
x y
4
3
1
0
-2
Infinite Solutions
State whether the given point is a solution to 3x - y = 5.
1) (2, 1)
2) (4, 5)
3) (-3, -14)
4)
5) (-1, 2)
€
12
,−312
⎛ ⎝
⎞ ⎠
3(2) - 1 = 5 Yes
3(4) - 5 = 5 No
3(-3) - -14 = 5 Yes
€
312 ⎛ ⎝
⎞ ⎠− −3
12
= 5 Yes
3(-1) - 2 = 5 No
Complete the chart and graph.
y = 2x - 3x y
-3-2-1 0 1 2 3
2(-3) - 3 = -92(-2) - 3 = -7-5-3-113
x
y
Complete the chart and graph.
y = 2x - 3x y
-3-2-1 0 1 2 3
2(-3) - 3 = -92(-2) - 3 = -7-5-3-113
x
y
Complete the chart and graph.
y = 2x - 3x y
-3-2-1 0 1 2 3
2(-3) - 3 = -92(-2) - 3 = -7-5-3-113
x
y
Complete the chart and graph.
y = 2x - 3x y
-3-2-1 0 1 2 3
2(-3) - 3 = -92(-2) - 3 = -7-5-3-113
x
y
Complete the chart and graph.
y = 2x - 3x y
-3-2-1 0 1 2 3
2(-3) - 3 = -92(-2) - 3 = -7-5-3-113
x
y
Complete the chart and graph.
y = 2x - 3x y
-3-2-1 0 1 2 3
2(-3) - 3 = -92(-2) - 3 = -7-5-3-113
7
2
€
272 ⎛ ⎝
⎞ ⎠− 3 =4 This line represents all
real solutions to y = 2x - 3.
x
y
1) 2x + y = 5 2) -x + 2y = -4-2x -2x
y = -2x + 5
+x +x2y = x - 42 2
yx
=−42
y x= −12
2
yx
= +−
242
Solve the following equations for y. (Function Form)
3) 3x + 5y = 10 4) -2x + 3y = -6-3x -3x
5y = -3x + 105 5
yx
=− +3 10
5
+2x +2x
Rewrite the equation in function form.
yx
=−
+35
105
y x=− +35
2
3y = 2x - 63 3
yx
= +−2
363
y x= −23
2
yx
=−2 63
Solve the equation for y, complete the chart, and graph.
1) 3x + 2y = 4-3x -3x
2y = -3x + 42 2
yx
=− +3 4
2
yx
=−
+32
42
y x=− +32
2
x y
-4
-2
0
2
4
6
8
5
2
-1
-4
-7
x
y
Rewrite in function form, complete the chart, and graph.
2) x - 3y = 6-x -x
-3y = -x + 6-3 -3
yx
=− +−
63
yx
=−−
+−363
y x= −13
2
x y
-6
-3
0
3
6
9
-4
-3
-2
-1
0
1
x
y
Solve the equation for y, find at least five solutions, and graph.
3) x + 2y = 8-x -x
2y = -x + 82 2
yx
=− +82
yx
=−
+2
82
y x=− +12
4
x y
-4
-2
0
2
4
6
6
5
4
3
2
1
x
y