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 Question from Nancy, a student: calculate the gradient of the line AB when the line AB is passing through the points A (2,1,) and B ( 4, -3).

Hi Nancy,

I wan to illustrate using two different points $(-2, 1)$ and $(5, 7).$ First I drew a diagram drew the line through he two points.

I also drew a horizontal line through $(-2, 1)$ and a vertical line through $(5, 7)$ meeting at $P.$ What are the coordinates of $P?$

The slope of the line through the two points $(-2, 1)$ and $(5, 7)$ is defined as the rise over the run where the rise is the length of the blue line segment in my diagram and the run is the length of the red line segment. I get the slope as

$\frac67 = 0.851.$

The gradient and the slope measure the same quaintly but the gradient is usually presented as a percentage. To convert $0.851$ to a percentage you multiply by $100$ and hence the gradient of the line through $(-2, 1)$ and $(5, 7)$ is $85.1 \%.$

Penny

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