Linear Functions Presentation

Linear Equations
Definition: an equation for a straight line.
In this lesson, you will:
a.) learn what slope-intercept form is
b.) learn how to find the slope of a line
c.) learn how to write these linear equations
d.) have a quiz over the concepts learn.
When you are ready to move on during this lesson, select the
arrow in the bottom right-hand corner.

Concepts
Select any concept to begin. Starting with slope-intercept form would be
best.
1. Slope-Intercept Form
2. How to Find Slope
3. Writing Linear Equations
4. Review and Quiz
When you would like to come back to this screen and try a new
concept, click on the home button in the bottom left-hand corner.

Slope-Intercept Form
The most-used form of a linear function.
Slope-Intercept Form : y=mx+b
(x,y) - any point that makes the equation true
m- is the slope of the line
b- the y-intercept

Slope of a line (m)
What is slope?
A: Slope is how steep a line is.
Slope can be positive or negative as shown below.

Y-Intercept
The point on a graph where the function crosses the y-axis.

Review Question
Which graph has a negative slope?
(Click the graph to answer)

Sorry, Incorrect
You selected the positive slope graph.
Select the “previous” arrow below to try-again.

Correct!
The graph you selected has a negative slope.
Select the “next” button to continue.

Review Question
Click on the location of the y-intercept.

Sorry, Incorrect
You did not click on the y-intercept.
Remember: the y-intercept is the location the graph crosses the y-axis.
Click the “previous arrow to try-again.

Correct!
You selected the y-intercept.
You have successfully gone through this concept, select “home”
to move onto a new concept

How to Find Slope
First, remember that slope is how steep a line is.
Also, you could have a positive or negative slope in a
linear equation.

Slope Formula
Slope (m)=
To find slope, you need two points (x1, y2) and (x2, y2)
Commonly referred to as
rise
run
y2 - y1
x2 - x1

Using the Slope Formula
How to use the formula
Step 1: Insert the two points into the formula. It does not matter which
point is point one and vice versa.
y2 - y2
x2 - x1
Slope Formula:
Step 2: Simplify

Example
Find the slope between the two points.
(Showing that either point could be point 1 or 2)
Step 1: Use the slope formula
Step 2: Simplify Slope=
Point 1: (3,2)
Point 2: (6,3)
y2 - y1
x2 - x1
=
3- 2
6 -3
1
3
Point 1: (6,3)
Point 2: (3,2)
y- y2 1
=
x- x2 1
2 -3
3- 6
1
3

Example
Find the slope between the two points:
Point 1: (-3,4)
Point 2: (2,1)
Step 1: Use the slope formula
y2 - y1
x2 - x1
Step 2: Simplify Slope=
=
1- 4
2 -(-3)
3
5

“Slope Dude” Video
Click here to watch a video that goes over slope once more.
Once complete, select the “next” button to move onto
Some review questions.

Review Question
Find the slope between the two points and select your answer.
Point 1: (-5,6) Point 2: (7,4)
A. Slope= -6
B. Slope= 11/3
C. Slope = 1/6

A. Slope= -6 is not correct
Remember: slope =
y2 - y2
x2 - x1
Try-again by selecting the “previous” button

B. Slope= 11/3 is not correct
Remember: slope =
y2 - y2
x2 - x1

C. Slope= 1/6 is correct
Slope =
4 - 6
7-(-5)
=
-2
-12
=
1
6
Select the “next” button to do one more question over slope.

Review Question
Find the slope between the two points and select your answer.
Point 1: (2,1) Point 2: (-3,4)
A. Slope= -3/5
B. Slope= 5/3
C. Slope = -5/3

A. Slope= -3/5 is correct
Slope =
4-1
-3- 2
=
-3
5
Select the “home” button to move onto a new concept.

B. Slope= 5/3 is not correct
Remember: slope =
y2 - y2
x2 - x1

C. Slope= -5/3 is not correct
Remember: slope =
y2 - y2
x2 - x1

Writing Linear Equations
There are two ways that I will show you how to write a
linear equation. The two ways are:
1. By using slope and a point
2. Using two points
Click on the arrow to learn how to write a linear
equation by using slope and a point.

Writing a Linear Equation
Using slope and one point-
What you need to find: the y-intercept
Step 1: Plug- in the given information into the slope-intercept form.
Slope- Intercept form: y=mx+b
Step 2: Solve for b, your y-intercept.
Step 3: Re-write the equation with your new found y-intercept in
slope-intercept form.

Example
Write an equation in slope-intercept form using the given
slope and y-intercept.
Point: (-4,3) Slope: 1/2
Step 1: Plug-in given information.
Step 2: Solve for b (y-intercept).
Step 3: Re-write equation.
y =
1
2
x + 4
b = 4
y =
1
2
x + 4

Writing a Linear Equation
Using two points-
What you need to find: slope and the y-intercept
Step 1: Use the given two points and the slope formula to find slope
Slope =
Step 2: Use the found slope and one point to find the y-intercept,
using the the slope- intercept form.
Step 3: Re-write the equation with your new found slope and y-intercept
in slope-intercept form.
y2 - y2
x2 - x1

Example
Write an equation in slope-intercept form using the two
given points.
Point 1: (-4,3) Point 2: (5,2)
What you need to find: the slope y-intercept
Step 1: Find the slope.
y = 4x +-14
Step 2: Find the y-intercept.
Step 3: Re-write the equation.
b = 4 b =
1
3
y =
1
3
x +
1
3

Review Question
y= -2x +10 y= 4x+ -8
y= 4x+ -14 y= 3x +6
Which equation has a point of (3, -2)
and a slope of 4?
Press the space bar to see the correct answer.
____________________

Help!
Step 1: Plug- in the given information into the slope-intercept form.
Slope- Intercept form: y=mx+b
Step 2: Solve for b, your y-intercept.
Step 3: Re-write the equation with your new found y-intercept in
slope-intercept form.
Select the “previous” button to go back and try-gain.

Answer: y= 4x+ -14
Step 1: Use the given information.
Step 2: Solve for the y-intercept.
-2 = 4(3)+b
b = -14
y = 4x +-14

Review Question
y=3x +-2/3 y= -1/2 x + 9/2
y=1/3 x + 5 y=-2x + -3
Which equation is found by using
the points (3,3) and (-1,5)?
Press the space bar to see the correct answer.
____________________

Help!
Using two points-
What you need to find: slope and the y-intercept
Step 1: Use the given two points and find the slope.
Step 2: Use the found slope and one point to find the y-intercept.
Step 3: Re-write the equation with your new found slope and y-intercept
in slope-intercept form.

Answer: y= -1/2 x +6
Point 1: (3,3) Point 2: (-1,5)
Step 1: Find the slope.
Step 2: Find the y-intercept.
b =
9
2
y =
-1
2
x +
9
2
b =
Select the “home” button to go over a new concept.
9
2
y =
-1
2
x +
9
2

Review and Quiz
Let’s review the key concepts of this lesson.
• Slope-intercept form – y=mx+b
m-slope b- y-intercept
• Slope Formula - y2 - y1
x2 - x1

Quiz
Are you ready to begin?
You can review some more by clicking “home” if you would like.
If you are ready, click “next” to begin.

Question #1
Which graph has a positive slope?
(Click the graph to answer)

Sorry, Incorrect
You selected the negative slope graph.

Correct!
.

Question #2
Click on the location of the y-intercept.

Sorry, Incorrect

Correct!

Question #3
Find the slope between the two given points.
Point 1: (2,4) Point 2: (-5,3)
A. Slope= -7/3
B. Slope= 1/7
C. Slope= 1/3
D. Slope= -2/7

Question #4
Find the slope between the two given points.
Point 1: (2,4) Point 2: (-5,3)
A. y= -1/2 x +5
B. y= -2x +2
C. y=-2x -3
D. y= -1/2 x +7

Correct!
CONGRATULATIONS!
You have successfully completed this lesson and correctly answered
all of the quiz questions.
Click the “home” button to go back over the concepts or
hit the “esc” button to exit this lesson.

Linear Functions Presentation

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