Slope Calculator

About This Slope Calculator Tool

This interactive graph slope calculator is a perfect tool for teachers to demonstrate how to find the slope of an equation. It helps students understand the concept of "steepness" or rate of change in a fun, visual way, connecting the abstract formula to a concrete graph.

What is a Slope Calculator?

A slope calculator is an online tool that helps you determine the steepness of a line. In mathematics, this steepness is called slope. The tool uses the slope formula to calculate this value, which is often represented by the letter $m$. Our calculator can be used as a finding slope from two points calculator or a point slope form calculator by providing two coordinate pairs. Teachers can also demonstrate how a 1:100 slope calculator works by entering specific rise and run values.

How Does This Tool Work?

The core concept is simple: slope is "rise over run."

The "rise" is the vertical change (how much the line goes up or down) between two points. The "run" is the horizontal change (how much the line goes left or right). This tool takes two points you enter, calculates the rise and run, and then divides them to give you the slope. The graph shows the line and the rise/run visually, making it a powerful graphing calculator for understanding the concept.

Ideas for Using Slope Calculator in the Classroom

• Visualizing Steepness: Enter different points to show what a positive, negative, zero, and undefined slope looks like.
• Connecting to the Real World: Use real-world examples like the steepness of a hill, a wheelchair ramp, or a staircase. This can relate to the ramp slope calculator concept.
• Exploring Proportional Relationships: For older students, you can use this tool to introduce proportional relationships and the slope-intercept form calculator concept.
• Interactive Practice: Have students predict the slope before entering points. Is the line going to be steep or gentle? Up or down?

How to Calculate Slope ($m$)

The slope, denoted by $m$, is calculated using the following formula, which represents the "rise over run":

Here's a breakdown of the steps:

1. Step 1: Identify Your Two Points. Let's say you have two points: Point 1 with coordinates $(x_1,y_1)$ and Point 2 with coordinates $(x_2,y_2)$.
2. Step 2: Calculate the "Rise". The rise is the change in the vertical or y-values. You find this by subtracting the y-coordinate of the first point from the y-coordinate of the second point.

Rise = $y_2-y_1$

3. Step 3: Calculate the "Run". The run is the change in the horizontal or x-values. You find this by subtracting the x-coordinate of the first point from the x-coordinate of the second point.

Run = $x_2-x_1$

4. Step 4: Divide Rise by Run. The final step is to divide your rise value by your run value. This gives you the slope, $m$.

$m=\frac{\text{Rise}}{\text{Run}}=\frac{y_2-y_1}{x_2-x_1}$

A few special cases to remember:

• If the run is zero ($x_2-x_1=0$), the line is vertical, and the slope is undefined.
• If the rise is zero ($y_2-y_1=0$), the line is horizontal, and the slope is zero.

When Do Students Learn About Slope in School?

While the formal concept of slope is introduced in middle school (6th-8th grade), the foundational ideas are present in elementary grades. This tool can be used to prepare students for these future lessons. Here are some of the key academic standards this tool supports:

Common Core Standards (CCSS):

• 8.EE.B.5: Graph proportional relationships, interpreting the unit rate as the slope of the graph.
• 8.F.B.4: Construct a function to model a linear relationship between two quantities. Determine the rate of change and initial value from a description of a relationship or from two (x, y) values.
• MP.4: Model with mathematics. Students apply what they know to solve problems, often using graphs and formulas.

Next Generation Science Standards (NGSS):

• MS-PS3-1: Construct and interpret graphical displays of data to describe the relationships of kinetic energy to the mass of an object and to the speed of an object. (Connects to graphing and rates of change)
• 4-ESS2-1: Make observations to provide evidence of the effects of weathering or the rate of erosion by water, ice, wind, or vegetation. (Connects to the concept of slope in a physical context, like a ramp or hill.)

Slope Calculator Worked Examples

Let's find the slope for a few points:

• Example 1: Point 1 at $(2,3)$ and Point 2 at $(4,7)$. The rise is $7-3=4$. The run is $4-2=2$. The slope is $\frac{4}{2}=2$.
• Example 2: Point 1 at $(0,5)$ and Point 2 at $(5,0)$. The rise is $0-5=-5$. The run is $5-0=5$. The slope is $\frac{-5}{5}=-1$.
• Example 3: A horizontal line. Point 1 at $(-2,4)$ and Point 2 at $(3,4)$. The rise is $4-4=0$. The run is $3-(-2)=5$. The slope is $\frac{0}{5}=0$.