Algebra Tutorials!
   
Home
About Us




TUTORIALS:

Absolute Values
Solving Two-Step Equations Algebraically
Multiplying Monomials
Factoring Trinomials
Solving Quadratic Equations
Power Functions and Transformations
Composition of Functions
Rational Inequalities
Equations of Lines
Graphing Logarithmic Functions
Elimination Using Multiplication
Multiplying Large Numbers
Multiplying by 11
Graphing Absolute Value Inequalities
Polynomials
The Discriminant
Reducing Numerical Fractions to Simplest Form
Addition of Algebraic Fractions
Graphing Inequalities in Two Variables
Adding and Subtracting Rational Expressions with Unlike Denominators
Multiplying Binomials
Graphing Linear Inequalities
Properties of Numbers and Definitions
Factoring Trinomials
Relatively Prime Numbers
Point
Inequalities
Rotating a Hyperbola
Writing Algebraic Expressions
Quadratic and Power Inequalities
Solving Quadratic Equations by Completing the Square
BEDMAS & Fractions
Solving Absolute Value Equations
Writing Linear Equations in Slope-Intercept Form
Adding and Subtracting Rational Expressions with Different Denominators
Reducing Rational Expressions
Solving Absolute Value Equations
Equations of a Line - Slope-intercept form
Adding and Subtracting Rational Expressions with Unlike Denominators
Solving Equations with a Fractional Exponent
Simple Trinomials as Products of Binomials
Equivalent Fractions
Multiplying Polynomials
Slope
Graphing Equations in Three Variables
Properties of Exponents
Graphing Linear Inequalities
Solving Cubic Equations by Factoring
Adding and Subtracting Fractions
Multiplying Whole Numbers
Straight Lines
Solving Absolute Value Equations
Solving Nonlinear Equations
Factoring Polynomials by Finding the Greatest Common Factor
Logarithms
Algebraic Expressions Containing Radicals 1
Addition Property of Equality
Three special types of lines
Quadratic Inequalities That Cannot Be Factored
Adding and Subtracting Fractions
Coordinate System
Solving Equations
Factoring Polynomials
Solving Quadratic Equations
Multiplying Radical Expressions
Solving Quadratic Equations Using the Square Root Property
The Slope of a Line
Square Roots
Adding Polynomials
Arithmetic with Positive and Negative Numbers
Solving Equations
Powers and Roots of Complex Numbers
Adding, Subtracting and Finding Least Common Denominators
What the Factored Form of a Quadratic can tell you about the graph
Plotting a Point
Solving Equations with Variables on Each Side
Finding the GCF of a Set of Monomials
Completing the Square
Solving Equations with Radicals and Exponents
Solving Systems of Equations By Substitution
Adding and Subtracting Rational Expressions
Percents
Laws of Exponents and Dividing Monomials
Factoring Special Quadratic Polynomials
Radicals
Solving Quadratic Equations by Completing the Square
Reducing Numerical Fractions to Simplest Form
Factoring Trinomials
Writing Decimals as Fractions
Using the Rules of Exponents
Evaluating the Quadratic Formula
Rationalizing the Denominator
Multiplication by 429
Writing Linear Equations in Point-Slope Form
Multiplying Radicals
Dividing Polynomials by Monomials
Factoring Trinomials
Introduction to Fractions
Square Roots
   
Try the Free Math Solver or Scroll down to Tutorials!

 

 

 

 

 

 

 

 
 
 
 
 
 
 
 
 

 

 

 
 
 
 
 
 
 
 
 

Please use this form if you would like
to have this math solver on your website,
free of charge.


Writing Linear Equations in Point-Slope Form

Objective Learn how to write equations for lines given information such as the slope and a point on the line, or two points on the line.

There are a number of ways to write equations representing straight lines. This lesson introduces two of them. The point-slope form can be written if the slope of the line in question and a point on the line are given, or if two points on the line are given. The standard form is also useful because it can be used to represent any line, even a vertical one. Vertical lines cannot be given in point-slope form since their slope is not defined.

 

Point-Slope Form

Key Idea

If we have a straight line, and we choose any two different points on it, we will get the same value for the slope no matter what points we choose.

Now draw a line like the one shown on the figuer below.

Display some points on the line, such as (1, 2) and (2, 4), in addition to the origin (0, 0). Then, try to find the slope of this line (it is actually 2). We write the general point P = ( x , y ), where x and y are variables. "How can you tell from the coordinates x and y whether P lies on the line?"

Remember that if (0, 0) and ( x , y ) are used to compute the slope, the answer still must be 2, since the key idea states that we will get the same answer no matter which two points are chosen.

You can find the slope by dividing the rise by the run. Since the rise is y and the run is x , slope

We know that the slope of this line is 2, so .

So, the rise is twice the run, and y = 2x for any point on this line. This equation holds for the coordinates of any point on the line.

There are many equations that describe the same line. We could have computed the slope using (x, y) and any other point on the line, such as (1, 2), as shown below.

 
(y - 2) = 2( x - 1) Multiply each side by x - 1.

Try to write your own equations for the line, using various points, such as (2, 4) or (3, 6).

Here are some more examples. Determine the slope and write an equation for each line graphed.

 

Example 1

Write an equation for the line.

Solution

The line has slope 3. One equation for it is y = 3x .

 

Example 2

Write an equation for the line.

Solution

The line has slope and an equation for it is .

So, if the slope of a line (let's call it m) and a single point (let's call it ( x 0 , y 0 )) on that line are known, then the following equation for the line can be written.

( y - y 0 ) = m ( x - x 0 )

This equation is said to be in point-slope form since it uses only information about one point and the slope.

Now, work on the following excercises.

Exercises

Find an equation in point-slope form for each line.

1. the line with slope 4 going through the point (1, 2)

( y - 2) = 4( x - 1)

2. the line with slope  1 going through the point (5, 4)

( y - 4) = -1( x - 5)

3. the line with slope going through the point (0, 10)

The slope and a single point on the line determine the whole line. Intuitively, the steepness and one point determine the line. This can be illustrated by rotating a ruler through a single point, and tracing out many of the possible slopes.

 

Copyrights © 2005-2017
Tuesday 17th of October