# 7.4 The slope-intercept form of a line

 Page 1 / 4
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 more familiar with the general form of a line, be able to recognize the slope-intercept form of a line, be able to interpret the slope and intercept of a line, be able to use the slope formula to find the slope of a line.

## Overview

• The General Form of a Line
• The Slope-Intercept Form of a Line
• Slope and Intercept
• The Formula for the Slope of a Line

## The general form of a line

We have seen that the general form of a linear equation in two variables is $ax+by=c$ (Section [link] ). When this equation is solved for $y$ , the resulting form is called the slope-intercept form. Let's generate this new form.

$\begin{array}{rrrr}\hfill ax+by& \hfill =& c\hfill & \hfill \text{Subtract}\text{\hspace{0.17em}}ax\text{\hspace{0.17em}}\text{from both sides}\text{.}\\ \hfill by& \hfill =& -ax+c\hfill & \hfill \text{Divide}\text{\hspace{0.17em}}both\text{\hspace{0.17em}}\text{sides by}\text{\hspace{0.17em}}b\\ \hfill \frac{by}{b}& \hfill =& \frac{-ax}{b}+\frac{c}{b}\hfill & \hfill \\ \hfill \frac{\overline{)b}y}{\overline{)b}}& \hfill =& \frac{-ax}{b}+\frac{c}{b}\hfill & \hfill \\ \hfill y& \hfill =& \frac{-ax}{b}+\frac{c}{b}\hfill & \hfill \\ \hfill y& \hfill =& \frac{-ax}{b}+\frac{c}{b}\hfill & \hfill \end{array}$

This equation is of the form $y=mx+b$ if we replace $\frac{-a}{b}$ with $m$ and constant $\frac{c}{b}$ with $b$ . ( Note: The fact that we let $b=\frac{c}{b}$ is unfortunate and occurs beacuse of the letters we have chosen to use in the general form. The letter $b$ occurs on both sides of the equal sign and may not represent the same value at all. This problem is one of the historical convention and, fortunately, does not occur very often.)

The following examples illustrate this procedure.

Solve $3x+2y=6$ for $y$ .

$\begin{array}{rrrr}\hfill 3x+2y& \hfill =& 6\hfill & \hfill \text{Subtract 3}x\text{\hspace{0.17em}}\text{from both sides}\text{.}\\ \hfill 2y& \hfill =& -3x+6\hfill & \text{Divide both sides by 2}\text{.}\hfill \\ \hfill y& \hfill =& -\frac{3}{2}x+3\hfill & \hfill \end{array}$

This equation is of the form $y=mx+b$ . In this case, $m=-\frac{3}{2}$ and $b=3$ .

Solve $-15x+5y=20$ for $y$ .

$\begin{array}{rrr}\hfill -15x+5y& \hfill =& 20\hfill \\ \hfill 5y& \hfill =& \hfill 15x+20\\ \hfill y& \hfill =& 3x+4\hfill \end{array}$

This equation is of the form $y=mx+b$ . In this case, $m=3$ and $b=4$ .

Solve $4x-y=0$ for $y$ .

$\begin{array}{rrr}\hfill 4x-y& \hfill =& 0\hfill \\ \hfill -y& \hfill =& -4x\hfill \\ \hfill y& \hfill =& 4x\hfill \end{array}$

This equation is of the form $y=mx+b$ . In this case, $m=4$ and $b=0$ . Notice that we can write $y=4x$ as $y=4x+0$ .

## The slope-intercept form of a line $y=mx+b$

A linear equation in two variables written in the form $y=mx+b$ is said to be in slope-intercept form.

## Sample set a

The following equations are in slope-intercept form:

$\begin{array}{cc}y=6x-7.& \text{In}\text{\hspace{0.17em}}\text{this}\text{\hspace{0.17em}}\text{case}\text{\hspace{0.17em}}m=6\text{\hspace{0.17em}}\text{and}\text{\hspace{0.17em}}b=-7.\end{array}$

$\begin{array}{cc}y=-2x+9.& \text{In}\text{\hspace{0.17em}}\text{this}\text{\hspace{0.17em}}\text{case}\text{\hspace{0.17em}}m=-2\text{\hspace{0.17em}}\text{and}\text{\hspace{0.17em}}b=9.\end{array}$

$\begin{array}{cc}y=\frac{1}{5}x+4.8& \text{In}\text{\hspace{0.17em}}\text{this}\text{\hspace{0.17em}}\text{case}\text{\hspace{0.17em}}m=\frac{1}{5}\text{\hspace{0.17em}}\text{and}\text{\hspace{0.17em}}b=4.8.\end{array}$

steps of developing a software
Present
win
bamori project
Rajendra
which approach used to reduce number of test cases
I wish to ask what is the mean of a data model
explanation of working of computer
hi
Moshiur
Hi
Malak
Hi
Yaw
How are you friends
Malak
Hlo nice too me
win
Thank for all fri
win
what's going on
lean for anything
win
hi guys
Ateke
hello.
Martins
hola como estas hey
Nurullohon
hi
MS
What is software engineering
good hi
MS
explain basic path testing for triangle problem?
Sorry
Mo
laptop ka meaning kaya hai
hii bro
MOHD
hi
hi
Juhi
hi how are u doing bro
what you have?
Are you all Indians?
no I am ethiopian
I am a cameroonian
Ateke
please how can I design a game
manojsunani
Manoj
આ આ
Manoj
પોતાના
Manoj
JOHNBULL
EJE
how can supported ; learn me
win
learn trained tO me.
tech
what is software engineering
software engineering are company manage
mahefuj
Text editor project in c++
Sreenu
hello sir
Ranjith
are unmanned flying machines that are built and equipped with various kinds of software systems that allow them to see, hear, and act. Discuss some of the societal challenges of building such kinds of systems.
You have developed a prototype of a software system and your manager is very impressed by it. She proposes that it should be put into use as a production sys tem, with new features added as required. This avoids the expense of system dev immediately useful. Write a short report for your manager expl
johni
You have developed a prototype of a software system and your manager is very impressed by it. She proposes that it should be put into use as a production sys tem, with new features added as required. This avoids the expense of system dev immediately useful.
johni
You have developed a prototype of a software system and your manager is very impressed by it. She proposes that it should be put into use as a production sys tem, with new features added as required. This avoids the expense of system dev immediately useful.
johni
You have developed a prototype of a software system and your manager is very impressed by it. She proposes that it should be put into use as a production sys tem, with new features added as required. This avoids the expense of system dev immediately useful. Write a short report for your manager expl
johni
You have developed a prototype of a software system and your manager is very impressed by it. She proposes that it should be put into use as a production sys tem, with new features added as required. This avoids the expense of system dev immediately useful.
johni
what is cocomo ?
?
StReeT
cocomo is cocote mo
Trixie
It means constructive cost model
Boris
HI
Masdul
hlo
Anuj
...
Moshiur
hello..
Moshiur
give me coding of these projects
feasibility study&fact gathering techniques
Please keep in mind that it's not allowed to promote any social groups (whatsapp, facebook, etc...), exchange phone numbers, email addresses or ask for personal information on QuizOver's platform.