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Basic Slope Exercise

Slope is a term used to indicate the steepness of a straight line. The greater the absolute value of this number, the steeper the line will be. Consider some of the examples of slope you are already familiar with such as the slope of a crater a Mars Rover must navigate, a black diamond ski trail or a ladder leaning against a building.

If you draw a line with two points on it (say, A and B) there are two numbers attached to this pair of points called the rise and the run. The rise is how much higher B is than A in the vertical direction. The run is how far over from A point B is in the horizontal direction. Slope is the value of the quotient of the rise divided by the run.

B

A

Slope distance = rise over run

Things to remember about slope:

• The slope is the same for any pair of points on the same line.
• Horizontal lines have a rise equal to zero. The slope is calculated by the rise of zero divided by a positive number (run) which equals zero.
• Vertical lines have an undefined slope because the run is always zero and division by zero is undefined.
• Lines with positive slope rise to the right. For positive slopes, the larger the number, the more steeply the line slopes upward.
• Lines with negative slope rise to the left. For negative slopes, the larger the absolute value of the negative number, the more steeply the line slopes downward.

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Get Ready

Start the MathTrax application.

Select the “Equations” tab at the top of the MathTrax application

Define an Equation

Type the equation y=x in the “Enter Equation” box.

Press Return

View Graph

Identify x-axis and y-axis

Identify origin

Calculate the slope of the line using the slope equation Slope=rise divided by run

Check your answer by reading the text description of the line

Change the Slope

Change your equation to y=2x

Calculate the slope of the line using the slope equation Slope=rise divided by run

Check you answer by reading the text description of the line