Graphing Linear Equations Objectives The student will be able to: EA 4.7- 1. graph linear functions. 2. write equations in standard form.
Dec 25, 2015
Section 4.5: Graphing Linear Equations
ObjectivesThe student will be able to:
EA 4.7- 1. graph linear functions.
2. write equations in standard form.
Solving for Linear Equations
• In order for us to solve and GRAPH linear equations, we need to review solving linear equations (from chapter 3)…
• Each (most) problems will have two variables, x and y.
• You will always solve for y! Remember we must undo to solve for y… let’s review.
Graphing Steps
1) Isolate the variable (solve for y).
2) Make a t-table. If the domain is not given, pick your own values:
(-2, -1, 0, 1, 2) for x values.
3) Plot the points on a graph.
4) Connect the points.
1) Review: Solve for y 2x + y = 4
1. Draw “the river”
2. Subtract 2x from both sides
- 2x - 2x
y = -2x + 42) Solve for y: 4x + 2y = -6
1. Subtract 4x
2. Simplify
3. Divide both sides by 2
4. Simplify
- 4x - 4x
2y = -4x - 6
2 2
y = -2x - 3
3) Solve for y: x - 3y = 6
1. Subtract x
2. Simplify
3. Divide both sides by -3
4. Simplify
- x - x
-3y = -x + 6
-3 -36
3
xy
2
3
xy
or
4) Review: Make a t-tableIf f(x) = 2x + 4, complete a table using the domain {-2, -1, 0, 1, 2}.
2(-2) + 4 = 0 (-2, 0)
2(-1) + 4 = 2 (-1, 2)
2(0) + 4 = 4 (0, 4)
2(1) + 4 = 6 (1, 6)
2(2) + 4 = 8 (2, 8)
x f(x)-2
-1
0
1
2
ordered pair
5) Given the domain {-2, -1, 0, 1, 2},
graph 3x + y = 6
-3(-2) + 6 = 12 (-2, 12)
-3(-1) + 6 = 9 (-1, 9)
-3(0) + 6 = 6 (0, 6)
-3(1) + 6 = 3 (1, 3)
-3(2) + 6 = 0 (2, 0)
x -3x + 6 ordered pair
1. Solve for y: 3x + y = 6
Subtract 3x - 3x - 3x
y = -3x + 62. Make a table
-2
-1
0
1
2
Bonus questions!What is the x-intercept?
(2, 0)What is the y-intercept?
(0, 6)Does the line increase or decrease?
Decrease
6) Given the domain {-2, -1, 0, 1, 2},
graph 3x + y = 63. Plot the points
(-2,12), (-1,9), (0,6), (1,3), (2,0)
4. Connect the points.
Standard FormAx + By = C
A, B, and C have to be integers
An equation is LINEAR (the graph is a straight line) if it can be written in standard form.
This form is useful for graphing (later on…).
Linear Equations
• To be LINEAR:
• No exponents
• No variables multiplied together Ex. xy = 4
• No variables in the denominator (bottom)
• CAN have y = #, Example: y = 4
• Look at the next slide for examples =>
Here’s the cheat sheet! An equation that is linear does NOT contain the following:
1. Variables in the denominator
2. Variables with exponents
3. Variables multiplied with other variables.
xy = 12
32y
x
2 3y x
8) Determine whether each equation is a linear equation.
1) 4x = 7 + 2y
Can you write this in the form
Ax + By = C?
4x - 2y = 7
A = 4, B = -2, C = 7
This is linear!
2) 2x2 - y = 7Can you write it in standard form?
NO - it has an exponent!Not linear
3) x = 12x + 0y = 12
A = 1, B = 0, C = 12Linear
9. Determine whether each equation is a linear equation.
Warm Up, copy the Agenda
• Solve the following for y:
• 1. x = 4y
• 2. 2x + 3y = 44
• 3. 2x + y = 104
• 4. x – 2y = 2
• 5. x – y = -3
• 6. x – y = 10
1) Review: Solve for y 2x + y = 4
1. Draw “the river”
2. Subtract 2x from both sides
- 2x - 2x
y = -2x + 42) Solve for y: 4x + 2y = -6
1. Subtract 4x
2. Simplify
3. Divide both sides by 2
4. Simplify
- 4x - 4x
2y = -4x - 6
2 2
y = -2x - 3
3) Solve for y: x - 3y = 6
1. Subtract x
2. Simplify
3. Divide both sides by -3
4. Simplify
- x - x
-3y = -x + 6
-3 -36
3
xy
2
3
xy
or
5) Review: Make a t-tableIf f(x) = 2x + 4, complete a table using the domain {-2, -1, 0, 1, 2}.
2(-2) + 4 = 0 (-2, 0)
2(-1) + 4 = 2 (-1, 2)
2(0) + 4 = 4 (0, 4)
2(1) + 4 = 6 (1, 6)
2(2) + 4 = 8 (2, 8)
x f(x)-2
-1
0
1
2
ordered pair
Steps:
• So first step is to SOLVE FOR Y
• Plug in the x values (to get y)
• Label points (x, y)
• Graph either points or double check with graphing calculator!
• You are done.