Slope Formula Program

Overview: In this program, you’ll let the user see the slope of a line when the user supplies two points.

Background:

The slope of a line is determined by dividing the rise by the run. (Rise over Run).

The rise is found by subtracting the second y from the first y. (or y1 – y2).

The run is found by subtracting the second x from the first x. (or x1 – x2).

Slope is often referred to by the letter m in mathematics.

Specifics:

First, you should have a title screen. Show the name of the program (make up something), class information, and your name. Use the SLEEP command to show this on the screen for about 2 or 3 seconds.

Second, your screen should clear and the program purpose/directions should follow. Explain what the program does and tell the user what is expected of them. Use the SLEEP command to pause for a few seconds while the user reads.

Third, the user should have to enter information about the first point (x1 and y1).

Fourth, the user should have to enter information about the second point (x2 and y2).

Next, the program should compute the slope of the line.

Finally, the program should report results to the user. The two points should show as part of the report. (See sample below).

Sample I/O:

Enter the first point:

X1? 4

Y1? 3

Enter the second point:

X2? 6

Y2? 7

The slope of the line between ( 4 , 3 ) and ( 6 , 4 ) would be 2.

Slope Formula Program – Version 2

Overview: When you have two spots, you can find the distance between them. This is true whether the spots are two points on a grid (like the slope program) or two locations on the Earth, like Auburn and Linwood.

Lots of programs rely on finding the distance between two points. Think about the modern navigation systems that are in new cars. These navigation systems use programs that need to know where you are now (by GPS) and where you are going to give you directions. On the Earth, every location is determined by longitude and latitude, which is really just a grid.

Another use of this is in web sites that provide mapping, like MapQuest or Google Maps. These sites run programs that calculate distances.

You can adjust your SLOPE program so that it calculates distance as well. The distance formula is a little trickier, but still workable.

Calculating Distances:

To find the distance between two points, you must first find out how much space is between them vertically and horizontally.

Examine the points (-3,5) and (8, 2). The first number in each pair shows how far “over” each point is. So, the first point is -3 units over and the second point is 8 units over. The number of units (horizontally) between these two is 11. The second number in each pair shows how far “up” the point is. The first point is 5 units up and the second point is only 2 units up. The number of units (vertically) between these two is 3 units.

So, the two points are 11 units apart horizontally and 3 units apart vertically. To find the distance between, you have to square both numbers. 11 squared is 121 and 3 squared is 9.

Next, you add the squares. 121 + 9 = 130.

Finally, you take the square root of the result. The square root of 130 is about 11.4. So, the distance is 11.4 units.

Specifics:

Adjust your slope program so that it calculates distance. You’ll need to research how to do square roots. The distance formula can be written in an expression as this:

Distance = sqrt( (x1-x2)^2 + (y1–y2)^2)