Free Algebra
Tutorials!
Home
Miscellaneous Equations
Operations with Fractions
Undefined Rational Expressions
Inequalities
Writing Equations for Lines Using Sequences
Intersections of Lines and Conics
Graphing Linear Equations
Solving Equations with Log Terms and Other Terms
Quadratic Expresions - Complete Squares
Adding and Subtracting Fractions with Like Denominators
Multiplying a Fraction by a Whole Number
Solving Equations with Log Terms and Other Terms
Solving Quadratic Equations by Factoring
Locating the Solutions of the Quadratic Equation
Properties of Exponents
Solving Equations with Log Terms on Each Side
http:
Graphs of Trigonometric Functions
Estimating Products and Quotients of Mixed Numbers
Inequalities
The circle
Adding Polynomials
Adding Fractions with Unlike Denominators
Factoring Polynomials
Linear Equations
Powers of Ten
Straight Lines
Dividing With Fractions
Multiplication Property of Equality
Rationalizing Denominators
Multiplying And Dividing Fractions
Distance Between Points on a Number Line
Solving Proportions Using Cross Multiplication
Using the Quadratic Formula
Scientific Notation
Imaginary Numbers
Values of Symbols for Which Fractions are Undefined
Graphing Equations in Three Variables
Writing Fractions as Decimals
Solving an Equation with Two Radical Terms
Solving Linear Systems of Equations by Elimination
Factoring Trinomials
Positive Rational Exponents
Adding and Subtracting Fractions
Negative Integer Exponents
Rise and Run
Brackets
Multiplying Square Roots
Multiplying Polynomials
Solving Systems of Linear Inequalities
Multiplication Property of Radicals
A Quadratic within a Quadratic
Graphing a Linear Equation
Calculations with Hundreds and Thousands
Multiplication Property of Square and Cube  Roots
Solving Equations with One Log Term
The Cartesian Coordinate Plane
Equivalent Fractions
Adding and Subtracting Square Roots
Solving Systems of Equations
Exponent Laws
Solving Quadratic Equations
Factoring Trinomials
Solving a System of Three Linear Equations by Elimination
Factoring Expressions
Adding and Subtracting Fractions
The parabola
Computations with Scientific Notation
Quadratic Equations
Finding the Greatest Common Factor
Introduction to Fractions
Simplifying Radical Expressions Containing One Term
Polynomial Equations
Graphing and Intercepts
The Number Line
Adding and Subtracting Rational Expressions with Different Denominators
Scientific Notation vs Standard Notation
Powers
Factoring by Grouping
Extraneous Roots
Variables and Expressions
Linera Equations
Integers and Substitutions
Squares and Square Roots
Adding and Subtracting Rational Expressions with Different Denominators
Solving Linear Inequalities
Expansion of a Product of Binomials
Powers and Exponents
Finding The Greatest Common Factor
Quadratic Functions
The Intercepts of a Parabola
Solving Equations Containing Rational Expressions
http:
Subtracting Polynomials
Solving Equations
Adding Fractions with Unlike Denominators
Solving Systems of Equations by Substitution
Solving Equations
Product and Quotient of Functions
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.


Rise and Run

Example 1

Find the rise and the run in moving from point P1 to point P2 on the graph.

Note: In P1(x1, y1), the P stands for “point” and the small 1 written a bit below and to the right of P indicates point 1. The small 1 is called a subscript. It is part of the name for the point.

Solution

We may find the rise and the run in two ways.

Use the graph:

• To find the run, on the graph count the number of units of horizontal change when moving from P1 to P2.

The run is 7.

• To find the rise, count the number of vertical units when moving from P1 to P2. The rise is 4.

Use algebra:

The coordinates of P1 are (-3, 1).

The coordinates of P2 are (4, 5).

• To find the rise, subtract the y-coordinates. That is, find y2 - y1.
 rise = y2 - y1 = 5 - 1 = 4
Note that the y-coordinate of the starting point, y1, is subtracted from the y-coordinate of the ending point, y2.

• To find the run, subtract the x-coordinates. That is, find x2 - x1.

 rise = x2 - x1 = 4 - (-3) = 4 + 3  = 7

Example 2

 a. Use the graph to find the rise and the run in moving from (-2, 1) to (4, -3).

b. Use the graph to find the rise and the run in moving the other way, from (4, -3) to (-2, 1).

Solution a. We are starting at (-2, 1) and moving to (4, -3).

To find the rise, count the number of vertical units when moving from (-2, 1) to (4, -3).

The rise is -4.

To find the run, count the number of horizontal units when moving from (-2, 1) to (4, -3).

The run is 6.

b. We are starting at (4, -3) and moving to (-2, 1).

To find the rise, count the number of vertical units when moving from (4, -3) to (-2, 1).

The rise is 4.

To find the run, count the number of horizontal units when moving from (4, -3) to (-2, 1).

The run is -6.

Note:

The run from (4, -3) to (-2, 1) is -6. This is the opposite of the run from (-2, 1) to (4, -3).

All Right Reserved. Copyright 2005-2024