<< Chapter < Page Chapter >> Page >
This module is from Elementary Algebra by Denny Burzynski and Wade Ellis, Jr. In this chapter the student is shown how graphs provide information that is not always evident from the equation alone. The chapter begins by establishing the relationship between the variables in an equation, the number of coordinate axes necessary to construct its graph, and the spatial dimension of both the coordinate system and the graph. Interpretation of graphs is also emphasized throughout the chapter, beginning with the plotting of points. The slope formula is fully developed, progressing from verbal phrases to mathematical expressions. The expressions are then formed into an equation by explicitly stating that a ratio is a comparison of two quantities of the same type (e.g., distance, weight, or money). This approach benefits students who take future courses that use graphs to display information.The student is shown how to graph lines using the intercept method, the table method, and the slope-intercept method, as well as how to distinguish, by inspection, oblique and horizontal/vertical lines. Objectives of this module: be able to find the equation of a line using either the slope-intercept form or the point-slope form of a line.

Overview

  • The Slope-Intercept and Point-Slope Forms

The slope-intercept and point-slope forms

In the pervious sections we have been given an equation and have constructed the line to which it corresponds. Now, however, suppose we're given some geometric information about the line and we wish to construct the corresponding equation. We wish to find the equation of a line.

We know that the formula for the slope of a line is m = y 2 - y 1 x 2 - x 1 . We can find the equation of a line using the slope formula in either of two ways:

If we’re given the slope, m , and any point ( x , 1 y 1 ) on the line, we can substitute this information into the formula for slope.
Let ( x , 1 y 1 ) be the known point on the line and let ( x , y ) be any other point on the line. Then

m = y - y 1 x - x 1 Multiply  both  sides  by x - x 1 . m ( x - x 1 ) = ( x - x 1 ) · y - y 1 x - x 1 m ( x - x 1 ) = y - y 1 For  convenience,  we'll  rewrite  the  equation . y - y 1 = m ( x - x 1 )

Since this equation was derived using a point and the slope of a line, it is called the point-slope form of a line.

Got questions? Get instant answers now!

If we are given the slope, m , y-intercept ,  ( 0 , b ) , we can substitute this information into the formula for slope.
Let ( 0 , b ) be the y-intercept  and  ( x , y ) be any other point on the line. Then,

m = y - b x - 0 m = y - b x Multiply  both  sides  by  x . m · x = x · y - b x m x = y - b Solve  for  y . m x + b = y For  convenience,   we'll  rewrite  this  equation . y = m x + b

Since this equation was derived using the slope and the intercept, it was called the slope-intercept form of a line.

Got questions? Get instant answers now!

We summarize these two derivations as follows.

Forms of the equation of a line

We can find the equation of a line if we’re given either of the following sets of information:
  1. The slope, m , and the y -intercept,  ( 0 , b ) , by substituting these values into

    y = m x + b

    This is the slope-intercept form.

  2. The slope, m , and any point, ( x 1 , y 1 ) , by substituting these values into

    y - y 1 = m ( x - x 1 )

    This is the point-slope form.

Questions & Answers

A golfer on a fairway is 70 m away from the green, which sits below the level of the fairway by 20 m. If the golfer hits the ball at an angle of 40° with an initial speed of 20 m/s, how close to the green does she come?
Aislinn Reply
cm
tijani
what is titration
John Reply
what is physics
Siyaka Reply
A mouse of mass 200 g falls 100 m down a vertical mine shaft and lands at the bottom with a speed of 8.0 m/s. During its fall, how much work is done on the mouse by air resistance
Jude Reply
Can you compute that for me. Ty
Jude
what is the dimension formula of energy?
David Reply
what is viscosity?
David
what is inorganic
emma Reply
what is chemistry
Youesf Reply
what is inorganic
emma
Chemistry is a branch of science that deals with the study of matter,it composition,it structure and the changes it undergoes
Adjei
please, I'm a physics student and I need help in physics
Adjanou
chemistry could also be understood like the sexual attraction/repulsion of the male and female elements. the reaction varies depending on the energy differences of each given gender. + masculine -female.
Pedro
A ball is thrown straight up.it passes a 2.0m high window 7.50 m off the ground on it path up and takes 1.30 s to go past the window.what was the ball initial velocity
Krampah Reply
2. A sled plus passenger with total mass 50 kg is pulled 20 m across the snow (0.20) at constant velocity by a force directed 25° above the horizontal. Calculate (a) the work of the applied force, (b) the work of friction, and (c) the total work.
Sahid Reply
you have been hired as an espert witness in a court case involving an automobile accident. the accident involved car A of mass 1500kg which crashed into stationary car B of mass 1100kg. the driver of car A applied his brakes 15 m before he skidded and crashed into car B. after the collision, car A s
Samuel Reply
can someone explain to me, an ignorant high school student, why the trend of the graph doesn't follow the fact that the higher frequency a sound wave is, the more power it is, hence, making me think the phons output would follow this general trend?
Joseph Reply
Nevermind i just realied that the graph is the phons output for a person with normal hearing and not just the phons output of the sound waves power, I should read the entire thing next time
Joseph
Follow up question, does anyone know where I can find a graph that accuretly depicts the actual relative "power" output of sound over its frequency instead of just humans hearing
Joseph
"Generation of electrical energy from sound energy | IEEE Conference Publication | IEEE Xplore" ***ieeexplore.ieee.org/document/7150687?reload=true
Ryan
what's motion
Maurice Reply
what are the types of wave
Maurice
answer
Magreth
progressive wave
Magreth
hello friend how are you
Muhammad Reply
fine, how about you?
Mohammed
hi
Mujahid
A string is 3.00 m long with a mass of 5.00 g. The string is held taut with a tension of 500.00 N applied to the string. A pulse is sent down the string. How long does it take the pulse to travel the 3.00 m of the string?
yasuo Reply
Who can show me the full solution in this problem?
Reofrir Reply
Got questions? Join the online conversation and get instant answers!
Jobilize.com Reply

Get Jobilize Job Search Mobile App in your pocket Now!

Get it on Google Play Download on the App Store Now




Source:  OpenStax, Elementary algebra. OpenStax CNX. May 08, 2009 Download for free at http://cnx.org/content/col10614/1.3
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