5.6 Slope using coordinates

The formula for finding the slope of a straight line between (or through) two points is:

    \[m=\frac{y_2-y_1}{x_2-x_1}\]

One point has coordinates (x_1,y_1), the other has coordinates (x_2,y_2). It doesn’t matter which one is which, as long as whichever point is first on the top line is also first on the bottom line.

On the applet below you can click ‘show triangle’.

The top line of the fraction, y_2-y_1 means the difference between the y coordinates. It gives the rise. This gives the vertical side of the triangle. If the line segment is going down, this number is negative.

The bottom line of the fraction, x_2-x_1 gives the horizontal side of the triangle. This gives the run.

To enter slope, calculate the rise and the run, then input \frac{\text{rise}}{\text{run}}.

To use this applet, you will need to use the four arrow tool on the y axis to see the second point. Click and drag the y axis up or down to see the complete line segment. Slope may be entered as a fraction or as a decimal rounded to two decimal places.

Skill 3


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