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( −3 , 3 ) , ( 2 , −5 )

8 5

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( −2 , 4 ) , ( 3 , −1 )

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( −1 , −2 ) , ( 2 , 5 )

7 3

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( −2 , −1 ) , ( 6 , 5 )

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( 4 , −5 ) , ( 1 , −2 )

−1

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( 3 , −6 ) , ( 2 , −2 )

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Graph a Line Given a Point and the Slope

In the following exercises, graph the line given a point and the slope.

( −3 , 4 ) ; m = 3 2


The graph shows the x y-coordinate plane. The x-axis runs from -12 to 12. The y-axis runs from 12 to -12. A line passes through the points “ordered pair -3, 4” and “ordered pair -1, 1”.

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( −2 , 5 ) ; m = 5 4

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( −1 , −4 ) ; m = 4 3


The graph shows the x y-coordinate plane. The x-axis runs from -12 to 12. The y-axis runs from 12 to -12. A line passes through the points “ordered pair 2,0” and “ordered pair -1, -4”.

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( −3 , −5 ) ; m = 3 2

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Solve Slope Applications

In the following exercises, solve these slope applications.

Slope of a roof A fairly easy way to determine the slope is to take a 12-inch level and set it on one end on the roof surface. Then take a tape measure or ruler, and measure from the other end of the level down to the roof surface. You can use these measurements to calculate the slope of the roof. What is the slope of the roof in this picture?

The figure shows a wood board at a diagonal representing a side-view slice of a pitched roof. A vertical line segment with arrows on both ends measures the vertical change in height of the roof and is labeled “4 inches”. A level tool is in a horizontal position above the board and above it is a line segment with arrows on both ends labeled “12 inches”.

1 3

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What is the slope of the roof shown?

The figure shows a  diagonal side-view slice of a pitched roof. A ruler in vertical position is at the bottom of the roof segment and shows unit labels 1 through 8 and extends one further unit. A second ruler starts at the “7” label of the vertical ruler and extends horizontally until it hits the rising roof. The horizontal ruler has unit labels 1 through 11 and extends one further unit.
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Road grade A local road has a grade of 6% . The grade of a road is its slope expressed as a percent.

  1. Find the slope of the road as a fraction and then simplify the fraction.
  2. What rise and run would reflect this slope or grade?

3 50 rise = 3 ; run = 50

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Highway grade A local road rises 2 feet for every 50 feet of highway.

  1. What is the slope of the highway?
  2. The grade of a highway is its slope expressed as a percent. What is the grade of this highway?
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Everyday math

Wheelchair ramp The rules for wheelchair ramps require a maximum 1 inch rise for a 12 inch run.

  1. How long must the ramp be to accommodate a 24-inch rise to the door?
  2. Draw a model of this ramp.

  1. 288 inches (24 feet)
  2. Models will vary.

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Wheelchair ramp A 1-inch rise for a 16-inch run makes it easier for the wheelchair rider to ascend the ramp.

  1. How long must the ramp be to easily accommodate a 24-inch rise to the door?
  2. Draw a model of this ramp.
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Writing exercises

What does the sign of the slope tell you about a line?

Answers will vary.

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How does the graph of a line with slope m = 1 2 differ from the graph of a line with slope m = 2 ?

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Why is the slope of a vertical line undefined?

Answers will vary.

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Explain how you can graph a line given a point and its slope.

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Self check

After completing the exercises, use this checklist to evaluate your mastery of the objectives of this section.

.

On a scale of 1–10, how would you rate your mastery of this section in light of your responses on the checklist? How can you improve this?

Chapter review exercises

Use the Rectangular Coordinate System

Plot Points in a Rectangular Coordinate System

In the following exercises, plot each point in a rectangular coordinate system.

In the following exercises, plot each point in a rectangular coordinate system and identify the quadrant in which the point is located.

  1. ( −1 , −5 )
  2. ( −3 , 4 )
  3. ( 2 , −3 )
  4. ( 1 , 5 2 )

  1. III
  2. II
  3. IV
  4. I

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  1. ( 3 , −2 )
  2. ( −4 , −1 )
  3. ( −5 , 4 )
  4. ( 2 , 10 3 )
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Identify Points on a Graph

In the following exercises, name the ordered pair of each point shown in the rectangular coordinate system.

The graph shows the x y-coordinate plane. The axes run from -7 to 7. “a” is plotted at 5, 3, “b” at 2, -1, “c” at -3,-2, and “d” at -1,4.

  1. (5,3)
  2. (2,−1)
  3. (−3,−2)
  4. (−1,4)

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The graph shows the x y-coordinate plane. The axes run from -7 to 7. “a” is plotted at 2, 0, “b” at 0, -5, “c” at -4,0, and “d” at 0,3.

  1. (2,0)
  2. (0,−5)
  3. (−4,0)
  4. (0,3)

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Verify Solutions to an Equation in Two Variables

In the following exercises, find the ordered pairs that are solutions to the given equation.

Questions & Answers

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Anassong Reply
nano basically means 10^(-9). nanometer is a unit to measure length.
Bharti
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Damian Reply
absolutely yes
Daniel
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s. Reply
what is fullerene does it is used to make bukky balls
Devang Reply
are you nano engineer ?
s.
fullerene is a bucky ball aka Carbon 60 molecule. It was name by the architect Fuller. He design the geodesic dome. it resembles a soccer ball.
Tarell
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Damian
That is a great question Damian. best way to answer that question is to Google it. there are hundreds of applications for buck minister fullerenes, from medical to aerospace. you can also find plenty of research papers that will give you great detail on the potential applications of fullerenes.
Tarell
what is the Synthesis, properties,and applications of carbon nano chemistry
Abhijith Reply
Mostly, they use nano carbon for electronics and for materials to be strengthened.
Virgil
is Bucky paper clear?
CYNTHIA
so some one know about replacing silicon atom with phosphorous in semiconductors device?
s. Reply
Yeah, it is a pain to say the least. You basically have to heat the substarte up to around 1000 degrees celcius then pass phosphene gas over top of it, which is explosive and toxic by the way, under very low pressure.
Harper
Do you know which machine is used to that process?
s.
how to fabricate graphene ink ?
SUYASH Reply
for screen printed electrodes ?
SUYASH
What is lattice structure?
s. Reply
of graphene you mean?
Ebrahim
or in general
Ebrahim
in general
s.
Graphene has a hexagonal structure
tahir
On having this app for quite a bit time, Haven't realised there's a chat room in it.
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what's the easiest and fastest way to the synthesize AgNP?
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Cied
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I start with an easy one. carbon nanotubes woven into a long filament like a string
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many many of nanotubes
Porter
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Berger describes sociologists as concerned with
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Jeannette has $5 and $10 bills in her wallet. The number of fives is three more than six times the number of tens. Let t represent the number of tens. Write an expression for the number of fives.
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Need to simplify the expresin. 3/7 (x+y)-1/7 (x-1)=
Crystal Reply
. After 3 months on a diet, Lisa had lost 12% of her original weight. She lost 21 pounds. What was Lisa's original weight?
Chris Reply
Practice Key Terms 1

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Source:  OpenStax, Prealgebra. OpenStax CNX. Jul 15, 2016 Download for free at http://legacy.cnx.org/content/col11756/1.9
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