Top Banner
Linear Equations Block 43
29

Linear Equations Block 43. Linear Equations Linear equations are the simplest equations that you deal with. A linear equation is a mathematical expression.

Dec 22, 2015

Download

Documents

Milton Parks
Welcome message from author
This document is posted to help you gain knowledge. Please leave a comment to let me know what you think about it! Share it to your friends and learn new things together.
Transcript
Page 1: Linear Equations Block 43. Linear Equations Linear equations are the simplest equations that you deal with. A linear equation is a mathematical expression.

Linear Equations

Block 43

Page 2: Linear Equations Block 43. Linear Equations Linear equations are the simplest equations that you deal with. A linear equation is a mathematical expression.

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.

Page 3: Linear Equations Block 43. Linear Equations Linear equations are the simplest equations that you deal with. A linear equation is a mathematical expression.

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.

Page 4: Linear Equations Block 43. Linear Equations Linear equations are the simplest equations that you deal with. A linear equation is a mathematical expression.

Steps to Solve Linear Equations

Linear equations are the simplest

equations that you deal with.

Page 5: Linear Equations Block 43. Linear Equations Linear equations are the simplest equations that you deal with. A linear equation is a mathematical expression.

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.

Page 6: Linear Equations Block 43. Linear Equations Linear equations are the simplest equations that you deal with. A linear equation is a mathematical expression.

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

Page 7: Linear Equations Block 43. Linear Equations Linear equations are the simplest equations that you deal with. A linear equation is a mathematical expression.

Combine Like TermsExample: 3z + 5 + 2z = 12 + 4z

3z + 2z + 5 = 12 + 4z5z + 5 = 12 + 4z

5z -4z + 5 = 12 + 4z -4z z + 5 = 12

Page 8: Linear Equations Block 43. Linear Equations Linear equations are the simplest equations that you deal with. A linear equation is a mathematical expression.

Isolate the terms with the variableExample: 3z + 5 + 2z = 12 + 4z

z + 5 -5 = 12 -5 z = 7

Page 9: Linear Equations Block 43. Linear Equations Linear equations are the simplest equations that you deal with. A linear equation is a mathematical expression.

Check SolutionExample: 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

Page 10: Linear Equations Block 43. Linear Equations Linear equations are the simplest equations that you deal with. A linear equation is a mathematical expression.

Practice Solving Linear Equations

38 = z + 15

Page 11: Linear Equations Block 43. Linear Equations Linear equations are the simplest equations that you deal with. A linear equation is a mathematical expression.

Practice Solving Linear Equations

x + 3 = 8x + 19

Page 12: Linear Equations Block 43. Linear Equations Linear equations are the simplest equations that you deal with. A linear equation is a mathematical expression.

Practice Solving Linear Equations

6 =x

3

Page 13: Linear Equations Block 43. Linear Equations Linear equations are the simplest equations that you deal with. A linear equation is a mathematical expression.

Practice Solving Linear Equations

2

5x = 8

Page 14: Linear Equations Block 43. Linear Equations Linear equations are the simplest equations that you deal with. A linear equation is a mathematical expression.

Graphing Linear Equations: T-ChartSteps to solving a Linear Equation using a T-Chart.

Graph y = 2x + 1

Step 1: draw a chart that looks a bit like the letter "T"

Page 15: Linear Equations Block 43. Linear Equations Linear equations are the simplest equations that you deal with. A linear equation is a mathematical expression.

Graphing Linear Equations: T-ChartGraph y = 2x + 1

Step 2: Label the columns.

x y ( or 2x+1)

Page 16: Linear Equations Block 43. Linear Equations Linear equations are the simplest equations that you deal with. A linear equation is a mathematical expression.

Graphing Linear Equations: T-ChartGraph y = 2x + 1

Step 3: Select values for x, solve for y

x y ( or 2x+1)

1 2(1) + 1 or 3 0 2(0) + 1 or 1-1 2(-1) + 1 or- 1

Page 17: Linear Equations Block 43. Linear Equations Linear equations are the simplest equations that you deal with. A linear equation is a mathematical expression.

Graphing Linear Equations: T-ChartGraph y = 2x + 1

Step 4: Ordered pairs

x y ( or 2x+1) ordered pairs

1 2(1) + 1 or 3(1,3)

0 2(0) + 1 or 1(0,1)

-1 2(-1) + 1 or -1 (-1,-1)

Page 18: Linear Equations Block 43. Linear Equations Linear equations are the simplest equations that you deal with. A linear equation is a mathematical expression.

Graphing Linear Equations: T-ChartGraph y = 2x + 3

Step 5: Draw your coordinate axis

Page 19: Linear Equations Block 43. Linear Equations Linear equations are the simplest equations that you deal with. A linear equation is a mathematical expression.

Graphing Linear Equations: T-ChartGraph y = 2x + 3

Step 5: Draw your coordinate axis

Graph y = 2x + 1

ordered pairs(1,3) (0,1)(-1,-1)

Page 20: Linear Equations Block 43. Linear Equations Linear equations are the simplest equations that you deal with. A linear equation is a mathematical expression.

Practice Graphing Linear Equations

y = 7 – 5x

Page 21: Linear Equations Block 43. Linear Equations Linear equations are the simplest equations that you deal with. A linear equation is a mathematical expression.

Practice Graphing Linear Equations

y =5

3x − 2

Page 22: Linear Equations Block 43. Linear Equations Linear equations are the simplest equations that you deal with. A linear equation is a mathematical expression.

Practice Graphing Linear Equations

y = 3

Page 23: Linear Equations Block 43. Linear Equations Linear equations are the simplest equations that you deal with. A linear equation is a mathematical expression.

Practice Graphing Linear Equations

x = -2

Page 24: Linear Equations Block 43. Linear Equations Linear equations are the simplest equations that you deal with. A linear equation is a mathematical expression.

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.

Page 25: Linear Equations Block 43. Linear Equations Linear equations are the simplest equations that you deal with. A linear equation is a mathematical expression.

Linear Equations in 2 Variables

A specific straight line can be determined by specifying at least two distinct points that the line passes throughor it can be determined by giving one point that it passes through and somehow describing how “tilted” the line is.

Page 26: Linear Equations Block 43. Linear Equations Linear equations are the simplest equations that you deal with. A linear equation is a mathematical expression.

Slope Intercept

The one point is called the intercept or y-intercept. The “tilt” is called the slope.

Page 27: Linear Equations Block 43. Linear Equations Linear equations are the simplest equations that you deal with. A linear equation is a mathematical expression.

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.”

Page 28: Linear Equations Block 43. Linear Equations Linear equations are the simplest equations that you deal with. A linear equation is a mathematical expression.

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

Page 29: Linear Equations Block 43. Linear Equations Linear equations are the simplest equations that you deal with. A linear equation is a mathematical expression.

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