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

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

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

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

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

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

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

Practice Solving Linear Equations

38 = z + 15

Practice Solving Linear Equations

x + 3 = 8x + 19

Practice Solving Linear Equations

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6 =x

3

Practice Solving Linear Equations

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2

5x = 8

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"

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

Step 2: Label the columns.

x y ( or 2x+1)

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

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)

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

Step 5: Draw your coordinate axis

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)

Practice Graphing Linear Equations

y = 7 – 5x

Practice Graphing Linear Equations

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y =5

3x − 2

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 throughor 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