# 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.

what is variations in raman spectra for nanomaterials
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
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
How we are making nano material?
what is a peer
What is meant by 'nano scale'?
What is STMs full form?
LITNING
scanning tunneling microscope
Sahil
how nano science is used for hydrophobicity
Santosh
Do u think that Graphene and Fullrene fiber can be used to make Air Plane body structure the lightest and strongest. Rafiq
Rafiq
what is differents between GO and RGO?
Mahi
what is simplest way to understand the applications of nano robots used to detect the cancer affected cell of human body.? How this robot is carried to required site of body cell.? what will be the carrier material and how can be detected that correct delivery of drug is done Rafiq
Rafiq
what is Nano technology ?
write examples of Nano molecule?
Bob
The nanotechnology is as new science, to scale nanometric
brayan
nanotechnology is the study, desing, synthesis, manipulation and application of materials and functional systems through control of matter at nanoscale
Damian
Is there any normative that regulates the use of silver nanoparticles?
what king of growth are you checking .?
Renato
What fields keep nano created devices from performing or assimulating ? Magnetic fields ? Are do they assimilate ?
why we need to study biomolecules, molecular biology in nanotechnology?
?
Kyle
yes I'm doing my masters in nanotechnology, we are being studying all these domains as well..
why?
what school?
Kyle
biomolecules are e building blocks of every organics and inorganic materials.
Joe
anyone know any internet site where one can find nanotechnology papers?
research.net
kanaga
sciencedirect big data base
Ernesto
Introduction about quantum dots in nanotechnology
what does nano mean?
nano basically means 10^(-9). nanometer is a unit to measure length.
Bharti
do you think it's worthwhile in the long term to study the effects and possibilities of nanotechnology on viral treatment?
absolutely yes
Daniel
how did you get the value of 2000N.What calculations are needed to arrive at it
Privacy Information Security Software Version 1.1a
Good
A soccer field is a rectangle 130 meters wide and 110 meters long. The coach asks players to run from one corner to the other corner diagonally across. What is that distance, to the nearest tenths place.
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.
What is the expressiin for seven less than four times the number of nickels
How do i figure this problem out.
how do you translate this in Algebraic Expressions
why surface tension is zero at critical temperature
Shanjida
I think if critical temperature denote high temperature then a liquid stats boils that time the water stats to evaporate so some moles of h2o to up and due to high temp the bonding break they have low density so it can be a reason
s.
Need to simplify the expresin. 3/7 (x+y)-1/7 (x-1)=
. After 3 months on a diet, Lisa had lost 12% of her original weight. She lost 21 pounds. What was Lisa's original weight?