4.4 Understand slope of a line (Page 6/14)

Page 6 / 14

Graph the line passing through the point $(−1, −3)$ whose slope is $m = 4 .$

Solution

Plot the given point.

The graph shows the x y coordinate plane. The x and y-axes run from negative 5 to 5. The point (negative 1, negative 3) is plotted and labeled.

$\begin{matrix} Identify the rise and the run. & m & = & 4 \\ Write 4 as a fraction. & \frac{rise}{run} & = & \frac{4}{1} \\ rise & = & 4 run = 1 \end{matrix}$

Count the rise and run and mark the second point.

This figure shows how to graph the line passing through the point (negative 1, negative 3) whose slope is 4. The first step is to identify the rise and run. The rise is 4 and the run is 1. 4 divided by 1 is 4, so the slope is 4. Next we count the rise and run and mark the second point. To the right is a graph of the x y-coordinate plane. The x and y-axes run from negative 5 to 5. We start at the plotted point (negative 1, negative 3) and count the rise, 4. We reach the point negative 1, 1, which we plot. We then count the run from this point, which is 1. We reach the point (0, 1), which is plotted. The last step is to connect the two points with a line. We draw a line which passes through the points (negative 1, negative 3) and (0, 1).

Connect the two points with a line.

The graph shows the x y coordinate plane. The x and y-axes run from negative 5 to 5. A line passes through the plotted points (-1, -3) and (1,0).

You can check your work by finding a third point. Since the slope is $m = 4$ , it can be written as $m = \frac{−4}{−1}$ . Go back to $(−1, −3)$ and count out the rise, $−4$ , and the run, $−1$ .

Got questions? Get instant answers now!

Graph the line with the point $(−2, 1)$ and slope $m = 3$ .

The graph shows the x y coordinate plane. The x and y-axes run from negative 7 to 7. A line passes through the points (negative 2, 1) and (negative 1, 4).

Got questions? Get instant answers now!

Graph the line with the point $(4, −2)$ and slope $m = −2$ .

The graph shows the x y coordinate plane. The x and y-axes run from negative 7 to 7. A line passes through the points (4, negative 2) and (5, negative 4).

Got questions? Get instant answers now!

Solve slope applications

At the beginning of this section, we said there are many applications of slope in the real world. Let’s look at a few now.

The ‘pitch’ of a building’s roof is the slope of the roof. Knowing the pitch is important in climates where there is heavy snowfall. If the roof is too flat, the weight of the snow may cause it to collapse. What is the slope of the roof shown?

This figure shows a house with a sloped roof. The roof on one half of the building is labeled

Solution

$\begin{matrix} Use the slope formula. & m = \frac{rise}{run} \\ Substitute the values for rise and run. & m = \frac{9}{18} \\ Simplify. & m = \frac{1}{2} \\ The slope of the roof is \frac{1}{2} . \\ \begin{matrix} The roof rises 1 foot for every 2 feet of \\ horizontal run. \end{matrix} \end{matrix}$

Got questions? Get instant answers now!

Use [link] , substituting the rise = 14 and run = 24.

$\frac{7}{12}$

Got questions? Get instant answers now!

Use [link] , substituting rise = 15 and run = 36.

$\frac{5}{12}$

Got questions? Get instant answers now!

Have you ever thought about the sewage pipes going from your house to the street? They must slope down $\frac{1}{4}$ inch per foot in order to drain properly. What is the required slope?

This figure is a right triangle. One leg is negative one quarter inch and the other leg is one foot.

Solution

$\begin{matrix} Use the slope formula. & m = \frac{rise}{run} \\ m = \frac{- \frac{1}{4} inch}{1 foot} \\ m = \frac{- \frac{1}{4} inch}{12 inches} \\ Simplify. & m = - \frac{1}{48} \\ The slope of the pipe is - \frac{1}{48} . \end{matrix}$

The pipe drops 1 inch for every 48 inches of horizontal run.

Got questions? Get instant answers now!

Find the slope of a pipe that slopes down $\frac{1}{3}$ inch per foot.

$- \frac{1}{36}$

Got questions? Get instant answers now!

Find the slope of a pipe that slopes down $\frac{3}{4}$ inch per yard.

$- \frac{1}{48}$

Got questions? Get instant answers now!

Access these online resources for additional instruction and practice with understanding slope of a line.

Key concepts

Find the Slope of a Line from its Graph using m = rise run
1. Locate two points on the line whose coordinates are integers.
2. Starting with the point on the left, sketch a right triangle, going from the first point to the second point.
3. Count the rise and the run on the legs of the triangle.
4. Take the ratio of rise to run to find the slope.
Graph a Line Given a Point and the Slope
1. Plot the given point.
2. Use the slope formula $m = \frac{rise}{run}$ to identify the rise and the run.
3. Starting at the given point, count out the rise and run to mark the second point.
4. Connect the points with a line.
Slope of a Horizontal Line
- The slope of a horizontal line, $y = b$ , is 0.
Slope of a vertical line
- The slope of a vertical line, $x = a$ , is undefined

Practice makes perfect

Use Geoboards to Model Slope

In the following exercises, find the slope modeled on each geoboard.

The figure shows a grid of evenly spaced pegs. There are 5 columns and 5 rows of pegs. A rubber band is stretched between the peg in column 1, row 3 and the peg in column 5, row 2, forming a line.

$\frac{1}{4}$

Got questions? Get instant answers now!

The figure shows a grid of evenly spaced pegs. There are 5 columns and 5 rows of pegs. A rubber band is stretched between the peg in column 2, row 4 and the peg in column 5, row 2, forming a line.

Got questions? Get instant answers now!

The figure shows a grid of evenly spaced pegs. There are 5 columns and 5 rows of pegs. A rubber band is stretched between the peg in column 1, row 4 and the peg in column 4, row 2, forming a line.

$\frac{2}{3}$

Got questions? Get instant answers now!

The figure shows a grid of evenly spaced pegs. There are 5 columns and 5 rows of pegs. A rubber band is stretched between the peg in column 3, row 4 and the peg in column 5, row 1, forming a line.

Got questions? Get instant answers now!

The figure shows a grid of evenly spaced pegs. There are 5 columns and 5 rows of pegs. A rubber band is stretched between the peg in column 2, row 1 and the peg in column 4, row 4, forming a line.

$\frac{−3}{2} = - \frac{3}{2}$

Got questions? Get instant answers now!

The figure shows a grid of evenly spaced pegs. There are 5 columns and 5 rows of pegs. A rubber band is stretched between the peg in column 1, row 1 and the peg in column 5, row 4, forming a line.

$- \frac{2}{3}$

Got questions? Get instant answers now!

The figure shows a grid of evenly spaced pegs. There are 5 columns and 5 rows of pegs. A rubber band is stretched between the peg in column 2, row 2 and the peg in column 4, row 5, forming a line.

Got questions? Get instant answers now!

In the following exercises, model each slope. Draw a picture to show your results.

$\frac{2}{3}$

The figure shows a grid of evenly spaced pegs. There are 5 columns and 5 rows of pegs. A rubber band is stretched between the peg in column 2, row 5 and the peg in column 5, row 3, forming a line.

Got questions? Get instant answers now!

$\frac{3}{4}$

Got questions? Get instant answers now!

$\frac{1}{4}$

The figure shows a grid of evenly spaced pegs. There are 5 columns and 5 rows of pegs. A rubber band is stretched between the peg in column 1, row 4 and the peg in column 5, row 3, forming a line.

Got questions? Get instant answers now!

$\frac{4}{3}$

Got questions? Get instant answers now!

$- \frac{1}{2}$

The figure shows a grid of evenly spaced pegs. There are 5 columns and 5 rows of pegs. A rubber band is stretched between the peg in column 1, row 4 and the peg in column 3, row 5, forming a line.

Got questions? Get instant answers now!

$- \frac{3}{4}$

Got questions? Get instant answers now!

$- \frac{2}{3}$

The figure shows a grid of evenly spaced pegs. There are 5 columns and 5 rows of pegs. A rubber band is stretched between the peg in column 1, row 2 and the peg in column 4, row 4, forming a line.

Got questions? Get instant answers now!

$- \frac{3}{2}$

Got questions? Get instant answers now!

Use $m = \frac{rise}{run}$ to find the Slope of a Line from its Graph

In the following exercises, find the slope of each line shown.

The graph shows the x y coordinate plane. The x and y-axes run from negative 10 to 10. A line passes through the points (negative 10, negative 8), (0, negative 4), and (10, 0).

$\frac{2}{5}$

Got questions? Get instant answers now!

The graph shows the x y coordinate plane. The x and y-axes run from negative 7 to 7. A line passes through the points (negative 2, negative 8) and (2, negative 2).

Got questions? Get instant answers now!

The graph shows the x y coordinate plane. The x and y-axes run from negative 7 to 7. A line passes through the points (negative 4, negative 6) and (4, 4).

$\frac{5}{4}$

Got questions? Get instant answers now!

The graph shows the x y coordinate plane. The x and y-axes run from negative 7 to 7. A line intercepts the y-axis at (0, negative 2) and passes through the point (3, 3).

Got questions? Get instant answers now!

The graph shows the x y coordinate plane. The x and y-axes run from negative 7 to 7. A line passes through the points (negative 3, 3) and (3, 1).

$- \frac{1}{3}$

Got questions? Get instant answers now!

The graph shows the x y coordinate plane. The x and y-axes run from negative 7 to 7. A line passes through the points (negative 2, 4) and (2, 2).

Got questions? Get instant answers now!

The graph shows the x y coordinate plane. The x and y-axes run from negative 7 to 7. A line intercepts the y-axis at (0, 6) and passes through the point (4, 3).

$- \frac{3}{4}$

Got questions? Get instant answers now!

The graph shows the x y coordinate plane. The x and y-axes run from negative 7 to 7. A line passes through the point (negative 3, 1) and intercepts the y-axis at (0, negative 1).

Got questions? Get instant answers now!

The graph shows the x y coordinate plane. The x and y-axes run from negative 7 to 7. A line passes through the points (negative 2, 1) and (2, 4).

$\frac{3}{4}$

Got questions? Get instant answers now!

The graph shows the x y coordinate plane. The x and y-axes run from negative 7 to 7. A line passes through the points (negative 1, 1) and (2, 3).

Got questions? Get instant answers now!

The graph shows the x y coordinate plane. The x and y-axes run from negative 7 to 7. A line passes through the points (negative 1, 6) and (1, 1).

$- \frac{5}{2}$

Got questions? Get instant answers now!

The graph shows the x y coordinate plane. The x and y-axes run from negative 7 to 7. A line passes through the point (negative 1, 3) and intercepts the x-axis at (3, 0).

Got questions? Get instant answers now!

The graph shows the x y coordinate plane. The x and y-axes run from negative 7 to 7. A line passes through the points (negative 2, 6) and (1, 4).

$- \frac{2}{3}$

Got questions? Get instant answers now!

The graph shows the x y coordinate plane. The x and y-axes run from negative 10 to 10. A line passes through the points (negative 1, 3) and (1, 2).

Got questions? Get instant answers now!

The graph shows the x y coordinate plane. The x and y-axes run from negative 10 to 10. A line intercepts the x-axis at (negative 2, 0) and passes through the point (2, 1).

$\frac{1}{4}$

Got questions? Get instant answers now!

The graph shows the x y coordinate plane. The x and y-axes run from negative 10 to 10. A line passes through the points (4, 2) and (7, 3).

Got questions? Get instant answers now!

Find the Slope of Horizontal and Vertical Lines

Questions & Answers

what is phylogeny

Odigie Reply

evolutionary history and relationship of an organism or group of organisms

AI-Robot

Deng

what is biology

Hajah Reply

the study of living organisms and their interactions with one another and their environments

AI-Robot

what is biology

Victoria Reply

HOW CAN MAN ORGAN FUNCTION

Alfred Reply

the diagram of the digestive system

Assiatu Reply

allimentary cannel

Ogenrwot

How does twins formed

William Reply

They formed in two ways first when one sperm and one egg are splited by mitosis or two sperm and two eggs join together

Oluwatobi

what is genetics

Josephine Reply

Genetics is the study of heredity

Misack

how does twins formed?

Misack

What is manual

Hassan Reply

discuss biological phenomenon and provide pieces of evidence to show that it was responsible for the formation of eukaryotic organelles

Joseph Reply

what is biology

Yousuf Reply

the study of living organisms and their interactions with one another and their environment.

Wine

discuss the biological phenomenon and provide pieces of evidence to show that it was responsible for the formation of eukaryotic organelles in an essay form

Joseph Reply

what is the blood cells

Shaker Reply

list any five characteristics of the blood cells

Shaker

lack electricity and its more savely than electronic microscope because its naturally by using of light

Abdullahi Reply

advantage of electronic microscope is easily and clearly while disadvantage is dangerous because its electronic. advantage of light microscope is savely and naturally by sun while disadvantage is not easily,means its not sharp and not clear

Abdullahi

cell theory state that every organisms composed of one or more cell,cell is the basic unit of life

Abdullahi

is like gone fail us

DENG

cells is the basic structure and functions of all living things

Ramadan

What is classification

ISCONT Reply

is organisms that are similar into groups called tara

Yamosa

in what situation (s) would be the use of a scanning electron microscope be ideal and why?

Kenna Reply

A scanning electron microscope (SEM) is ideal for situations requiring high-resolution imaging of surfaces. It is commonly used in materials science, biology, and geology to examine the topography and composition of samples at a nanoscale level. SEM is particularly useful for studying fine details,

Hilary

Got questions? Join the online conversation and get instant answers!

Jobilize.com Reply

<< Chapter < Page Page > Chapter >>

Practice Key Terms 7

Read also:

Get Jobilize Job Search Mobile App in your pocket Now!

100% Free Mobile Applications
Receive real-time job alerts and never miss the right job again

Source: OpenStax, Elementary algebra. OpenStax CNX. Jan 18, 2017 Download for free at http://cnx.org/content/col12116/1.2

Google Play and the Google Play logo are trademarks of Google Inc.

Notification Switch

Would you like to follow the 'Elementary algebra' conversation and receive update notifications?

Ask

	U.s. history By OpenStax Read Online Course
	37 Biology 37 The Endocrine System MCQ By OpenStax Start Quiz
	1 Psychology Concept Test By John Gabrieli Start Test
	Managerial Psychology Exam By Dan Ariely Start Exam
©flickr: Abraham	Multicellular Organisms Test By Monty Hartfield Start Test
	1 Week 1 Social Psych By Yacoub Jayoghli Start Quiz
	Professional Writing MCQ By Mary Cohen Start Quiz
	2 Sociology 02 Sociological Research MCQ By OpenStax Start Quiz
	46 Biology 46 Ecosystems MCQ By OpenStax Start Quiz
	Business Law Ethics By Kevin Moquin Start Quiz