# 11.4 Understand slope of a line  (Page 7/9)

 Page 7 / 9

$\left(-3,3\right),\left(2,-5\right)$

$-\frac{8}{5}$

$\left(-2,4\right),\left(3,-1\right)$

$\left(-1,-2\right),\left(2,5\right)$

$\frac{7}{3}$

$\left(-2,-1\right),\left(6,5\right)$

$\left(4,-5\right),\left(1,-2\right)$

−1

$\left(3,-6\right),\left(2,-2\right)$

Graph a Line Given a Point and the Slope

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

$\left(1,-2\right);m=\frac{3}{4}$

$\left(1,-1\right);m=\frac{1}{2}$

$\left(2,5\right);m=-\frac{1}{3}$

$\left(1,4\right);m=-\frac{1}{2}$

$\left(-3,4\right);m=-\frac{3}{2}$

$\left(-2,5\right);m=-\frac{5}{4}$

$\left(-1,-4\right);m=\frac{4}{3}$

$\left(-3,-5\right);m=\frac{3}{2}$

$\left(0,3\right);m=-\frac{2}{5}$

$\left(0,5\right);m=-\frac{4}{3}$

$\left(-2,0\right);m=\frac{3}{4}$

$\left(-1,0\right);m=\frac{1}{5}$

$\left(-3,3\right);m=2$

$\left(-4,2\right);m=4$

$\left(1,5\right);m=-3$

$\left(2,3\right);m=-1$

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 $\text{12-inch}$ 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?

$\frac{1}{3}$

What is the slope of the roof shown?

Road grade A local road has a grade of $\text{6%}.$ 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?

$\phantom{\rule{0.2em}{0ex}}\frac{3}{50}\phantom{\rule{0.2em}{0ex}}$ $\phantom{\rule{0.2em}{0ex}}\text{rise}=3;\phantom{\rule{0.2em}{0ex}}\text{run}=50$

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?

## 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 $\text{24-inch}$ rise to the door?
2. Draw a model of this ramp.

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

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

1. How long must the ramp be to easily accommodate a $\text{24-inch}$ rise to the door?
2. Draw a model of this ramp.

## Writing exercises

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

How does the graph of a line with slope $m=\frac{1}{2}$ differ from the graph of a line with slope $m=2?$

Why is the slope of a vertical line undefined?

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

## 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?

## Use the Rectangular Coordinate System

Plot Points in a Rectangular Coordinate System

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

$\left(1,3\right),\left(3,1\right)$

$\left(2,5\right),\left(5,2\right)$

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

1. $\phantom{\rule{0.2em}{0ex}}\left(-1,-5\right)$
2. $\phantom{\rule{0.2em}{0ex}}\left(-3,4\right)$
3. $\phantom{\rule{0.2em}{0ex}}\left(2,-3\right)$
4. $\phantom{\rule{0.2em}{0ex}}\left(1,\frac{5}{2}\right)$

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

1. $\phantom{\rule{0.2em}{0ex}}\left(3,-2\right)$
2. $\phantom{\rule{0.2em}{0ex}}\left(-4,-1\right)$
3. $\phantom{\rule{0.2em}{0ex}}\left(-5,4\right)$
4. $\phantom{\rule{0.2em}{0ex}}\left(2,\frac{10}{3}\right)$

Identify Points on a Graph

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

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

1. (2,0)
2. (0,−5)
3. (−4,0)
4. (0,3)

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

who was the first nanotechnologist
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Veysel
technologist's thinker father is Richard Feynman but the literature first user scientist Nario Tagunichi.
Veysel
Norio Taniguchi
puvananathan
Interesting
Andr
I need help
Richard
anyone have book of Abdel Salam Hamdy Makhlouf book in pdf Fundamentals of Nanoparticles: Classifications, Synthesis
what happen with The nano material on The deep space.?
It could change the whole space science.
puvananathan
the characteristics of nano materials can be studied by solving which equation?
sibaram
synthesis of nano materials by chemical reaction taking place in aqueous solvents under high temperature and pressure is call?
sibaram
hydrothermal synthesis
ISHFAQ
how can chip be made from sand
is this allso about nanoscale material
Almas
are nano particles real
yeah
Joseph
Hello, if I study Physics teacher in bachelor, can I study Nanotechnology in master?
no can't
Lohitha
where is the latest information on a no technology how can I find it
William
currently
William
where we get a research paper on Nano chemistry....?
nanopartical of organic/inorganic / physical chemistry , pdf / thesis / review
Ali
what are the products of Nano chemistry?
There are lots of products of nano chemistry... Like nano coatings.....carbon fiber.. And lots of others..
learn
Even nanotechnology is pretty much all about chemistry... Its the chemistry on quantum or atomic level
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da
no nanotechnology is also a part of physics and maths it requires angle formulas and some pressure regarding concepts
Bhagvanji
hey
Giriraj
Preparation and Applications of Nanomaterial for Drug Delivery
revolt
da
Application of nanotechnology in medicine
has a lot of application modern world
Kamaluddeen
yes
narayan
what is variations in raman spectra for nanomaterials
ya I also want to know the raman spectra
Bhagvanji
I only see partial conversation and what's the question here!
what about nanotechnology for water purification
please someone correct me if I'm wrong but I think one can use nanoparticles, specially silver nanoparticles for water treatment.
Damian
yes that's correct
Professor
I think
Professor
Nasa has use it in the 60's, copper as water purification in the moon travel.
Alexandre
nanocopper obvius
Alexandre
what is the stm
is there industrial application of fullrenes. What is the method to prepare fullrene on large scale.?
Rafiq
industrial application...? mmm I think on the medical side as drug carrier, but you should go deeper on your research, I may be wrong
Damian
STM - Scanning Tunneling Microscope.
puvananathan
how did you get the value of 2000N.What calculations are needed to arrive at it
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