Review Graphing Linear Equations

ReviewGraphing Linear Equations

A review of sections 4.2, 4.3, and 4.5

Mike HagedornCEP 811 STaIR

Standards

A3.1.1 Write the symbolic forms of linear functions (standard, point-slope, and slope-intercept) given appropriate information, and convert between forms.

A3.1.2 Graph lines (including those of the form x = h and y = k) given appropriate information.

A3.1.3 Relate the coefficients in a linear function to the slope and x- and y-intercepts of its graph.

Objectives

The learner will review the three different methods of graphing linear equations.

The learner will be given specific equations and/or story problems and will be forced to decide with method is the most efficient

Standards and Objectives

Introduction

This project is designed to allow students to review graphing linear equations on their own. Use this project as a way to prepare yourself for the test. Take your time and make sure you are fully comfortable with the content. There will be links throughout this project that will take you to various web pages and help clarify any misunderstandings.

DIRECTIONS

Go through each this project by clicking the arrows

Go through and review each method. If you need to review something, you may click the back button.

Once you have completed the review, complete the practice quiz and attempt to answer them correctly

If you feel you need to review some more, click the homebutton. There will also be various links throughout to help youwhich will be underlined in red for you to click on if needed

Move on to the next section

Vocabulary to know

Ordered pair

Linear equation

X-intercept

Y-intercept

Slope

Slope intercept form

Start with equation in two variables

Example:

A solution is the ordered pair that produces a true statement

Need several to be able to create a graph

Lets graph

First: make a table by choosing a few values for x

Second: substitute each x into the equation and find the value of y

Plot the corresponding points on a graph

Connect the points

Graph linear equations using tables

x-2-1012Y-7-5-3-11

Graph the following equation using a table

Lets use for our x values in our table to find the corresponding y values

The table as follows

2. Now lets plot the points and connect the dots

xy8

Lets practice

Graph linear equations using intercepts

Intercepts: the two points where the graph of the line crosses the axes

x-intercept: where the graph crosses the x-axis. Will have the ordered pair

y-intercept: where the graph crosses the y-axis. Will have the ordered pair

To find each intercept

To find x-intercept:To find y-intercept:

Let y = 0, Let x = 0,

then solve for xthen solve for y

Once you have the two intercepts, plot them on a graph and connect the dots! Theres the graph for that equation.

Find the intercepts of

x-int: Let y = 0

y-int: Let x = 0

So our is 7, and our is 2

Now lets graph this!

Example Solving and graphing interepts

Graph the following linear equation by finding the intercepts

Find the x-intercept (let y = 0)

Find the y-intercept (let x = 0)

Now plot the points (intercepts) on the graph

Lets practice

Graph linear equations using slope-intercept form

Easiest way to graph!!!!!!

The equation is:

Need to know the slope.

Can do this by counting the grid lines on a graph if graph is already there, OR

Using the equation if two points are known that lie on the line.

Will commonly be the coefficient or in other words, the number next to the x in most problems.

The other thing you need is the y-intercept

Is the constant term in the equation.

Example

Slope

y-intecept

First:

Get the equation into slope-intercept form (y by itself)

Second:

Plot the y-intercept on the graph

Third

From the y-intercept, apply the slope to get a second point, then connect the dots

Example: Graph ; follow the three steps

1. Already in slope-intercept form

2. Plot the y-intercept: b = 2

3. From y-intercept, apply slope

To graph using Slope-intercept form

Rise

Run

Graph the following equation using slope-intercept form

Get equation into slope-intercept form (get y by itself)

2. Plot y-intercept

3. Apply the slope from the y-intercept to get a second point

Lets practice

slope

y-intercept

Practice Quiz!!!!!!

Choose the correct letter for each question

Be sure took look closely at all information before selecting a choice

Take your time. Use pencil and paper if you need to

Which table matches the following graph

a)

b)

c)

d)

Problem #1

xy

xy

xy

xy

What is the x-intercept and y-intercept of the following equation?

a)x-intercept: 10 (10, 0)

y-intercept: -16 (0, -16)

b) x-intercept: -10 (-10, 0)

y-intercept: 16 (0, 16)

c)x-intercept: 8 (8, 0)

y-intercept: -5 (0, -5)

d)x-intercept: -8 (-8, 0)

y-intercept: 5 (0, 5)

Problem #2

Problem #3

Which graph matches the following x and y intercepts

a)

b)

c)

d)

The slope and y-intercept of the following graph are?

Slope (m):4

y-intercept (b):-7

Slope (m):-4

y-intercept (b):-7

Slope (m):4

y-intercept (b):7

Slope (m):-4

y-intercept (b):7

Problem #4

Problem #5

Which graph matches the following linear equation?

a)

b)

c)

d)

Be sure to check your math and watch your signs.

Try Again

Put in zero for one variable, then solve for the other

Try Again

Here is a video to help solve for the x and y intercept

20

Look closely at the signs of the values and match them on the graph

Try Again

Try counting the grid lines to help.

Try Again

Remember our steps to graph using slope-intercept form

Start with ?????, then apply????

Try Again

Great Job!!!!

Great Job!!!!

Great Job!!!!

Great Job!!!!

Great Job!!!!

Push for the next problem

Congratulations!!!!

You completed the tutorial and now are ready for the test.

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