Lines and Slopes

Table of Contents

• Introduction

• Drawing a Line

- Graphing Points First

• Slope

- Calculating Slope

- Finding Those Slopes

Introduction

John and his friend wants to catch flies with their tongues. Their tongues are going to go straight just how a line would. John begins to use his knowledge about lines to catch flies.

Drawing a Line

When you are able to know two points on a line then you are able to find the rest of the line. John is going to draw a line through these points.

John shifts his tongue to reach the two points and go right through them.

John begins to draw arrows to show that the line goes on forever.

*make sure you use a ruler or something with a straight edge to ensure

that your line is straight.*

Graphing Points First

When graphing a line you must use an equation. Take for example when graphing the line:

3x + y = 9 John would have to find the values x and y to make the equation true.

He choices to have x value equal 2. Once John has the value x, he has to find y by substituting the value x=2 into the equation.

3x + y = 9

3(2) + y = 9

6 + y = 9

-6 =-6

Y = 3

John realize that when x = 2, y = 3 which makes the equation true. Now

he graphs the point ( 2, 3)

(2, 3)

John needs one more point before graphing the line. So he has to find another value for x and y. He makes y = 0. He substitutes the value of y = 0 into the original equation.

(Shown below)

3x + y = 9

3x + 0 = 9

3x = 9

3 3

X = 3

Here John found that when y=0, x=3that makes the equation true. Now

graph the second point (3,0)

(2, 3)

(3, 0)

Again John draws a line through the points and add the arrows. Then write the equation beside the line to label it.

(2, 3)

(3, 0)

3x + y = 9

To be sure John understands how to graph a line. He graphs another equation:

y = 2x - 4

Y = 2x – 4

Y = 2(0) – 4

Y = 0 – 4

Y = -4

Again he has to find two points to graph the equation. He has to find the values for xand y to make sure the equation is true. For the first point he substitutes 0 for the variable x.

When John value x = 0 then y = -4. He can now graph the point (0, -4).

(0, -4)

For the second point he substitutes 1 for the variable x.

Y= 2x – 4

Y = 2(1) – 4

Y = 2 – 4

Y = -2

John value x = 1 then y = -2.

Now he can graph the second

point (1, -2).

(0, -4)

(1, -2)Y = 2x - 4

He draws the line through the

points and add the arrows. He

then labels the line with the

equation.

SlopeWhen using slope we use it to measure a line’s

slant.Here is a picture with three different types of slopes.

The green line has the biggest slope and the red line has the smallest slope out of the three slopes.

There can even

be a negative

slope line and

that’s when the

lines point down

instead of up.

Ex. Shown to

the right

Calculating the Slope

When calculating the slope John define the slope as the change in the y-coordinates divide by the change in the x-coordinates. Most people refer to it as the “rise over run”.

*The change in y-coordinate is

the “rise” and the change in the

x-coordinate is the “run”.*

Slope Formula

Change in x-coordinate and change in my y-coordinate is put in a formula using the Greek letter delta ∆. This is an abbreviation for change.

∆ Y∆ X

When identifying our points, our first point (x1, y1) and the second point (x2, y2). John substitute these points in for the delta ∆.

Y2 –Y1

X2 – Y1M=M=

Finding the Slope

John first have to locate the two points on the line. We notice that the line intersect at the y-axis. This is the first point (0, 4). When then find the second point on the line where the two gridlines cross. This is our second point (2, 1).

Now that we have our points John plugs it into the slope equation to find the slope.

M = (y2 – y1)/ (x2 – x1)

M = (1 – 4) / (2 – 0)

M = -3 / 2

The slope is negative.

Overall

John has taught us how to draw a line by graphing the points and calculating the slope. Know he and his friends can catch their flies.

Cited

This is the site where I found my lesson plan and some of my graphs.

• http://mathforum.org/cgraph/cslope/drawline.html

This is the site where I found some of my graphs.

• http://nghsapphysicsb.blogspot.com/2009/10/super-explanation-of-how-rolling.html