Math
» SlopeIntercept Form Line Equation «
The Circle
Reflection
Dilation
Translation
Rotation
The Multiplication Table
Factored Integers
Complex Numbers
Stirling Numbers
Numbers as Boolean Functions
Calculator TI89
Tower of Hanoi

Please support this site by giving a donation in the amount of your choosing. Send it to: tutor@sdmath.com via www.PayPal.com because with your help we can increase and improve the mathematical information you can find in here.
SlopeIntercept Form of the Line Equation
The slopeintercept form of a line’s equation, explicitly casts the variable y as a function of the variable x. The variable y appears all by itself on the lefthand side of the equation, while being absent from the righthand side.
The slopeintercept form of a line’s equation makes immediately apparent two of the most important features of a line in the XYplane: its slope and its Yintercept.
The slope is the m constant, the coefficient of x
The Yintercept is the b constant, the equation’s independent term
In the applet below, you can change the numerical values of b and m, and watch how these changes impact the location of the green line:
The red slider on the bottom left controls the m value, the slope of the line; while the blue slider on the bottom right controls the b value, the line's yintercept.
Moving the red slider makes the green line rotate around the point (0, b); while moving the blue slider makes the green line move up or down parallel to itself.
You can use this applet, and the other applet down below, to find the answers to many homework questions about straight lines given in the slopeintercept format.
The Yintercept
The Yintercept value b indicates the point (0, b), where the line crosses the Yaxis
 When the Yintercept is positive, the line crosses the Yaxis above the origin.
 When the Yintercept is negative, the line crosses the Yaxis below the origin.
 When the Yintercept is zero, the line passes through the origin.
For example, line { y = x + 3 } crosses the Yaxis at point (0, 3), that is 3 units above the origin;
while parallel line { y = x  2 } crosses the Yaxis at point (0, 2), that is 2 units below the origin.
When two lines have different slopes but the same Yintercept, they meet on the Yaxis, because them both cross the Yaxis at the exact same point (0, b).
A Formula for the Yintercept Given the Coordinates of Two Points on the Line
If a line with slopeintercept equation { y = mx + b } passes through two points P_{1} = (x_{1}, y_{1}), and P_{2} = (x_{2}, y_{2}),
you can use the following formula to calculate b, the line's yintercept:
For example, given the points (x_{1}, y_{1}) = (6,1) and (x_{2}, y_{2}) = (2, 3)
SlopeIntercept Interactive Applet with Three Movable Lines
Each line in the applet below has its slope and yintercept values controled not by sliders but by the point (m, b)
Each control point affects the position of the line of the same color, by means of that point's coordinates
 To change the slope of a line, move sideways the point of the same color
 To change the yintercept of a line, move up or down the point of the same color
A curious property of the (m, b) control point representation used in the above applet, is this:
 When the three control points are lined up along any nonvertical straight line, all three corresponding lines meet at a common point
 When the three control points are lined up along any vertical line, all three corresponding lines become parallel, since they all have the same slope m
The slope
The slope indicates how fast a general point on the line goes up as it moves to the right.
 When the slope is a positive number, the line goes up to the right, and down to the left.
 When the slope is negative, the line goes down to the right, and up to the left.
 When the slope is zero, the line is horizontal.
 When the slope has an absolute value greater than 1, the acute angle the line makes with the Xaxis is greater than 45º
 When the slope has an absolute value smaller than 1, the acute angle the line makes with the Xaxis is smaller than 45º
 A line with slope equal to 1 makes a 45º angle with the positive direction of the Xaxis
 A line with slope equal to 1 makes a 135º angle with the positive direction of the Xaxis
The farther away from zero the slope value is, the faster y changes in response to a change in x, for a general point (x, y) on the line. This means the line becomes steeper.
For example, in the line { y = 2x + 3 }, when x changes from 1 to 2, y changes from 5 to 7.
This means 2 units of change in y for each unit of change in x, according to the slope value m = 2.
Now, if we consider the line { y = 4x + 2 }, when x changes from 1 to 2, y changes from 6 to 10.
This is a change of 4 units in y for each unit of change in x, according to the slope value m = 4.
On the other hand, the closer to zero the slope is, the slower y changes in response to a change in x, for a general point (x, y) on the line. This means the line is less steep.
For example, in the line { y = 0.5x + 6 }, when x changes from 2 to 4, y changes from 7 to 8.
This means the variable x needs to go up by 2 units in order for the variable y to increase a single unit.
This line with a slope of 0.5 grows more slowly than a line with a slope of 1.
Differences of the slopeintercept form with other equation forms
In contrast with both the general form, and the standard form of the line’s equation, the slopeintercept form of the equation provides a unique representation of a line, because when two lines have either a different slope, or a different Yintercept, they really are two different lines.
In other words, if two equations in slopeintercept form have different coefficients, they do represent different lines. This stands in sharp contrast to the general form of the equation, where you can have many equations that look very different from each other, because they have different coefficients,

Tutoring
Home
FAQ
About the Tutor
Online Tutoring
Testimonials
For Parents
Rate & Contact Info
Links
=
=
=
Online Math Tutor
 Effective
 Proven
 Recommended
 Expert Tutor
 Homework Help
 Exam Preparation
 All Math Subjects
 K4 Through College
 Individual Sessions
 In Person
 Online Tutoring Available
 Excellent Results
 GMAT
 GRE
 CSET
 CBEST
 ELM
 CLEP
 SAT
 ACT
 CAHSEE
 ASVAB
 ASTB
 FBI phase II
 More...
 Pass Your Test!
 Improve Your Grades
 Get Back On Track
 Make Math Easier
 Understand Each Topic
 Get The Problems Right!
 Ensure Your Academic Success
