Algebra I Chapter 5: Equationsgruver.weebly.com/uploads/9/8/2/7/9827712/alg_i_chapter...Alg I...

Alg I Chapter 5 Notes.notebook

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December 05, 2013

Jun 109:21 AM

Algebra IChapter 5:

Writing Linear Equations

Jun 131:21 PM

Vocabulary

Chapter 5 Lesson 1Write Linear Equations in SlopeIntercept Form

Words to Review:

yintercept

slope

slopeintercept form


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Jun 109:24 AM

Example 1: Use Slope and yintercept to Write an Equation

Aug 281:44 PM

Example 2: Standardized Test Practice


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Aug 281:47 PM

Example 3: Write an Equation of a Line Given Two PointsEquation Given Two Points1. Calculate the slope. (change in y over the change in x)2. Determine what the yintercept is.3. Using y = mx + b, substitute the slope and the yintercept.

Sep 910:53 AM

Example 4: Write a Linear Function Equation Given Values of the Function1. Write the input and output values as ordered pairs. 2. Calculate the slope. (change in y over the change in x)3. Determine what the yintercept is.4. Using y = mx + b, substitute the slope and the yintercept.


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Sep 201:09 PM

Example 5: Solve a MultiStep Problem

Aug 282:08 PM

Chapter 5 Lesson 2Use Linear Equations in SlopeIntercept Form

Vocabulary

Words to Review:

yintercept

slope

slopeintercept form


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December 05, 2013

Aug 298:29 AM

Example 1: Write an Equation Given the Slope and a Point

Equation Given the Slope and a Point1. Identify the slope.2. Find the y intercept (b) by substituting the slope and point values of x and y into y = mx + b.3. Rewrite the equation in slope intercept form.

Aug 298:29 AM

Example 2: Write an Equation Given Two Points

Equation Given Two Points1. Calculate the slope. (change in y over the change in x)2. Find the y intercept (b) by substituting the slope and one of the point values into y = mx + b.3. Using y = mx + b, substitute the slope and the yintercept.


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Aug 298:29 AM

Example 3: Standardized Test Practice Equation Given Values of the Function1. Write the input and output values as ordered pairs. 2. Calculate the slope. (change in y over the change in x)3. Find the y intercept (b) by substituting the slope and one of the point values into y = mx + b.4. Using y = mx + b, substitute the slope and the yintercept.

Sep 201:11 PM



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Sep 201:11 PM


Aug 3012:52 PM

Chapter 5 Lesson 3Write Linear Equations in PointSlope FormVocabulary

If m = 4 and (3, 2),

then y 2 = 4(x 3)


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Aug 301:08 PM

Example 1: Write an Equation in PointSlope Form

Writing an Equation in PointSlope Form Given the Point and Slope1. Substitute the slope and point values of x and y into the equation. 2. Simplify any signs.

Aug 301:08 PM

Example 2: Graph an Equation in PointSlope Form

Graphing Given PointSlope Form1. Identify the point. (Remember to change the signs for x and y since the formula shows subtraction.)2. Plot the point.3. Use the slope to plot another point from the first one. (rise over run)4. Draw a line through the points.


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December 05, 2013

Aug 301:08 PM

Example 3: Use PointSlope Form to Write an Equation

Graphing Given PointSlope Form1. Identify the point. (Remember to change the signs for x and y since the formula shows subtraction.)2. Plot the point.3. Use the slope to plot another point from the first one. (rise over run)4. Draw a line through the points.

Sep 2412:46 PM

Example 5: Write a RealWorld Linear Model From a Table


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Aug 3012:52 PM

Chapter 5 Lesson 4Write Linear Equations in Standard Form

VocabularyWords to Review:

Standard Form Linear Equation

1. ax + bx = c (x and y are on the same side of the equation)

2. a, b, c are integers (positive and negative whole numbers no fractions or decimals!!)

3. The a term is usually positive.

Aug 301:55 PM

Example 1: Write Equivalent Equations in Standard Form Reminder:The properties of equality allow me to multiply and divide an equation AS LONG AS I DO IT TO BOTH SIDES OF THE EQUATION!


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Example 2: Write an Equation from a Graph Writing Standard Form Equation from Two Points

1. Calculate the slope.2. Use point slope form to write an equation.3. Rewrite the form in standard form:

ax + bx = c (x and y are on the same side of the equation) a, b, c are integers (positive and negative whole numbers no fractions or decimals!) the a term is usually positive

Aug 301:56 PM

Example 3: Write an Equation of a Line Reminders:

Horizontal Linesy = # (no x term)slope = 0Crosses the y axis!

Vertical Linesx = # (no y term)slope = undefined (something divided by 0)Crosses the x axis!


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Example 4: Complete an Equation in Standard Form Completing an Equation in Standard Form

1. Substitute the point values for x and y into the equation.2. Find the value of the missing variable.3. Substitute the found value back into the original equation.4. Make sure the equation is in standard form.

ax + bx = c (x and y are on the same side of the equation) a, b, c are integers (positive and negative whole numbers no fractions or decimals!) the a term is usually positive

Sep 201:25 PM


Find the number of people by substituting the known values.

Don't forget to identify variables!

Now, substitute the number of people into the original equation. Make sure it is in standard form.


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Aug 3012:52 PM

Chapter 5 Lesson 5Write Equations of Parallel and Perpendicular LinesVocabulary

The slopes of the lines will be opposite reciprocals.

Conditional:

Converse:

Sep 257:22 AM

Example 1: Write an Equation of a Parallel Line

Write an Equation of a Parallel Line Given an Equation and a Point1. Identify the slope. 2. Substitute this exact value in for the slope of y = mx + b.3. Find the y intercept by substituting the values of the point into y = mx + b.4. Rewrite the equation in slope intercept form by substituting the slope and y intercept into y = mx + b.


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Sep 2012:44 PM

Example 2: Determine Whether Lines are Parallel of Perpendicular

Determine if Lines are Parallel or Perpendicular1. Identify the slopes of the lines. (You can write the equation in slope intercept form to do this.)2. Determine if the lines are parallel or perpendicular:

exact same slopes lines are parallel opposite reciprocal slopes lines are perpendicular neither of the above lines are NOT parallel or perpendicular

Sep 201:32 PM

Example 3: Determine Whether Lines are Parallel of Perpendicular

Determine if Lines are Parallel or Perpendicular1. Identify the slopes of the lines. (You can write the equation in slope intercept form to do this.)2. Determine if the lines are parallel or perpendicular:

exact same slopes lines are parallel opposite reciprocal slopes lines are perpendicular neither of the above lines are NOT parallel or perpendicular


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Sep 201:32 PM

Example 4: Write an Equation of a Perpendicular Line

Write an Equation of a Perpendicular Line Given an Equation and a Point1. Identify the slope. Find the opposite reciprocal of that slope. This will be the slope of the

perpendicular line. 2. Substitute the new perpendicular slope in for the slope of y = mx + b.3. Find the y intercept by substituting the values of the point into y = mx + b.4. Rewrite the equation in slope intercept form by substituting the slope and y intercept into y = mx + b.

Aug 3012:52 PM

Chapter 5 Lesson 6Fit a Line to DataVocabulary


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Example 1: Describe the Correlation of Data

Look for an increase or a decrease as you read the graph from left to right.

Sep 201:34 PM

Example 2: Make a Scatter Plot 1. Plot the points.2. Look for an increase or a decrease as you read the graph from left to right.


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Example 3: Write an Equation to Model Data

You could also approximate the equation using the approximate slope and the approximate yintercept.

Sep 201:35 PM

Example 4: Interpret a Model


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Aug 3012:52 PM

Chapter 5 Lesson 7Predict with Linear ModelsVocabulary

Sep 2012:49 PM

Example 1: Interpolate Using an Equation Using a Graphing Calculator to Find a Best Fitting Line1. Touch the STAT button.2. Choose 1:Edit and touch ENTER.3. Enter the x values into the L1 column (list 1).4. Enter the y values into the L2 column (list 2).5. Touch the STAT button again.6. Choose CALC using the right arrow button.7. Choose 4:LinReg(ax+b) using the down arrow button and touch ENTER.8. Touch ENTER again. (a is the slope and b is the y intercept. Substitute those into y = mx + b.

(When entering years, use 1, 2, 3, etc.)


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Sep 201:37 PM

Example 2: Extrapolate Using an Equation Using a Graphing Calculator to Graph a Best Fitting Line1. Touch the y= button.2. Enter the equation for the best fitting line.3. Change your window settings by touching the WINDOW button.

Identify your domain and range for you Xmin, Xmax, Ymin, and Ymax. Make sure to go above and below these values to see more of the graph.

4. Touch GRAPH. This is the graph of the best fitting line.5. Touch TRACE to identify specific points on the line. You can use the left and right arrows.

While in TRACE, you can choose an input value by typing that number. If you hit ENTER, you will find the output for that input.

Reminder: These are years 6 and 7 according to your calculator.

Sep 201:37 PM

Example 4: Find the Zero of a Function

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