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Mathematics

Grade 9

Number patterns, graphs, equations,

Statistics and probability

Module 15

Finding the equation of a straight line graph from a diagram

ACTIVITY 1

To find the equation of a straight line graph from a diagram

[LO 2.5]

  1. If we can find out the values of m and c , then we simply substitute them in the general equation y = mc + c to give us the defining equation of the line. Let’s do an example from the given diagram.

To find c is easy as it is the value (positive or negative or zero) where the line cuts the y–axis. Substitute this value (it is –1) for c.

The equation now becomes y = mx – 1. To find the gradient (the value of m) we construct the right-angled triangle between two suitable points where the graph goes exactly through corners on the graph paper.

  • Remembering that m is a fraction:
change in vertical distance
change in horizontal distance
  • We read off the number of units of the height and the length of the triangle to give us the numerator and denominator respectively
  • We also have to decide whether the sign is negative or positive by looking at which way the line slopes.
  • This gives us: m = 4 6 = 2 3 size 12{ size 11{m```=``` - { { size 8{4} } over { size 8{6} } } ```=``` - { { size 8{2} } over { size 8{3} } } }} {} (remember to simplify the fraction).
  • This value is now substituted for m in the equation: y = 2 3 x 1 size 12{ size 11{y```=``` - ``` { { size 8{2} } over { size 8{3} } } x``` - ```1}} {} . This gives us the defining equation of the line in the diagram.
  • Going back to the previous section, use this method to find the defining equations of the eight graphs in the first two diagrams.

2 How do we deal with horizontal and vertical graphs? They are the easiest.

  • If the line is horizontal, then the equation is y = c . We have to replace the c by a value. We read this value off the graph – it is the y –intercept! Substitute this into y = c , and you have the defining equation.
  • If the line is vertical, the equation is x = k . Find k by reading from the graph where the line cuts the x –axis and substitute this number for k . This gives the defining equation.
  • From the previous section, find the equations for the four graphs in the last diagram.

Here are the answers: y = 1 and y = –1,5 are the two horizontal lines, and x = –1 and x = –2,5 are the two vertical lines.

3 The following diagrams have a mixture of lines for you to test your skills on.

4 Did you notice that the gradients ( m ) of lines G and H are the same? Why is this?

ACTIVITY 2

To calculate the gradient of a straight line from two points on the line

[LO 2.5]

  • If you know the coordinates of two points on a certain straight line, then you can draw that line, as you have seen. And from the sketch you can find the gradient as you have already learnt. But it is not necessary to have a graph to find the gradient.
  • Here is an example: The points (3 ; –1) and (4 ; 2) are on a certain straight line.
  • First we calculate the vertical distance between the two points by subtracting the second point’s y -coordinate from the first point’s y –coordinate. This is the numerator of the gradient.
  • Then we calculate the horizontal distance between the two points by subtracting the second point’s x -coordinate from the first point’s x -coordinate. This is the denominator of the gradient.
  • So, the gradient is: m = vertical distance horizontal distance = 1 2 3 4 = 3 1 = 3 size 12{ size 11{m``=`` { { size 11{"vertical"``"distance"}} over { size 11{"horizontal"```"distance"}} } ``=`` { { size 11{ - 1` - `2}} over { size 11{3 - 4}} } ``=`` { { size 11{ - 3}} over { size 11{ - 1}} } ``=`} size 13{`}3} {}

Questions & Answers

what is variations in raman spectra for nanomaterials
Jyoti Reply
I only see partial conversation and what's the question here!
Crow Reply
what about nanotechnology for water purification
RAW Reply
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
Brian Reply
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?
LITNING Reply
what is a peer
LITNING Reply
What is meant by 'nano scale'?
LITNING Reply
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 ?
Bob Reply
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?
Damian Reply
what king of growth are you checking .?
Renato
What fields keep nano created devices from performing or assimulating ? Magnetic fields ? Are do they assimilate ?
Stoney Reply
why we need to study biomolecules, molecular biology in nanotechnology?
Adin Reply
?
Kyle
yes I'm doing my masters in nanotechnology, we are being studying all these domains as well..
Adin
why?
Adin
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?
Damian Reply
research.net
kanaga
sciencedirect big data base
Ernesto
Introduction about quantum dots in nanotechnology
Praveena Reply
what does nano mean?
Anassong Reply
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?
Damian Reply
absolutely yes
Daniel
how did you get the value of 2000N.What calculations are needed to arrive at it
Smarajit Reply
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Source:  OpenStax, Mathematics grade 9. OpenStax CNX. Sep 14, 2009 Download for free at http://cnx.org/content/col11056/1.1
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