Download Linear Equations - Math GR. 6-8

Linear Equations
Block 43
Linear Equations
Linear equations are the simplest
equations that you deal with.
A linear equation is a mathematical
expression that has an equal sign and
linear expressions.
Linear Equations
A variable is a number that you don't
know, often represented by "x" or "y”.
A linear expression is a mathematical
statement that performs functions of
addition, subtraction, multiplication, and
division.
Steps to Solve Linear Equations
Linear equations are
the simplest
equations that you
deal with.
Steps to Solve Linear Equations
1. Combine like terms.
2. Isolate terms that contain the variable you
wish to solve for.
3. Isolate the variable you wish to solve for.
4. Substitute your answer into the original
equation to check that it works.
Combine Like Terms
Like terms are terms that contain the same
variable or group of variables raised to the same
exponent, regardless of their numerical
coefficient.
Example: 3z + 5 + 2z = 12 + 3z
Combine Like Terms
Example: 3z + 5 + 2z = 12 + 4z
3z + 2z + 5 = 12 + 4z
5z + 5 = 12 + 4z
5z -4z + 5 = 12 + 4z -4z
z + 5 = 12
Isolate the terms with the variable
Example: 3z + 5 + 2z = 12 + 4z
z + 5 -5 = 12 -5
z =7
Check Solution
Example: 3z + 5 + 2z = 12 + 4z
z=7
3z + 5 + 2z = 12 + 4z
3(7) + 5 + 2(7) = 12 +
4(7)21+ 5 + 14 = 12 + 28
40 = 40
Practice Solving Linear Equations
38 = z + 15
Practice Solving Linear Equations
x + 3 = 8x + 19
Practice Solving Linear Equations
x
6
3

Practice Solving Linear Equations
2
x8
5

Graphing Linear Equations: T-Chart
Steps to solving a Linear Equation using a TChart.
Graph y = 2x + 1
Step 1: draw a chart that looks a bit like the letter
"T"
Graphing Linear Equations: T-Chart
Graph y = 2x + 1
Step 2: Label the columns.
x
y ( or 2x+1)
Graphing Linear Equations: T-Chart
Graph y = 2x + 1
Step 3: Select values for x, solve for y
x
y ( or 2x+1)
1
0
-1
2(1) + 1 or 3
2(0) + 1 or 1
2(-1) + 1 or- 1
Graphing Linear Equations: T-Chart
Graph y = 2x + 1
Step 4: Ordered pairs
x
y ( or 2x+1)
1
0
-1
2(1) + 1 or 3
2(0) + 1 or 1
2(-1) + 1 or -1
ordered pairs
(1,3)
(0,1)
(-1,-1)
Graphing Linear Equations: T-Chart
Graph y = 2x + 3
Step 5: Draw your coordinate axis
Graph y = 2x + 1
Graphing Linear Equations: T-Chart
Graph y = 2x + 3
Step 5: Draw your coordinate axis
ordered pairs
(1,3)
(0,1)
(-1,-1)
Practice Graphing Linear Equations
y = 7 – 5x
Practice Graphing Linear Equations
5
y  x2
3

Practice Graphing Linear Equations
y=3
Practice Graphing Linear Equations
x = -2
Linear Equations in 2 Variables
The equation y = 2x – 1 produces a
graph that is a straight line.
This equation is one example of a
general class of equations called linear
equations in two variables.
The two variables are usually x and y.
Linear Equations in 2 Variables
A specific straight line can be determined
by specifying at least two distinct points
that the line passes through
or
it can be determined by giving one point
that it passes through and somehow
describing how “tilted” the line is.
Slope Intercept
The one point is called the intercept or
y-intercept.
The “tilt” is called the slope.
Slope
The slope of a line is a measure of how
“tilted” the line is.
For example, a highway sign might say
something like “6% grade ahead.”
Using Slope-Intercept
The slope-intercept form is the most frequent
way used to express an equation of a line.
If an equation is in slope-intercept form, it is
easy to graph.
Slope-Intercept form is y=mx+b.
m is slope and b is y-intercept
Using Slope-Intercept
The slope-intercept form is the most frequent
way used to express an equation of a line.
If an equation is in slope-intercept form, it is
easy to graph.
Slope-Intercept form is y=mx+b.
m is slope and b is y-intercept