Derive Point-Slope Formula

harpazo

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How do we derive the point-slope formula in the picture?

sDraw_2018-08-11_12-23-57.png
 

MarkFL

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Slope is defined as:

\(\displaystyle m=\frac{\Delta y}{\Delta x}=\frac{y_2-y_1}{x_2-x_1}\)

If we let the second point be the arbitrary point \((x,y)\), we then have:

\(\displaystyle m=\frac{y-y_1}{x-x_1}\)

This gives us the locus of all points that have a slope of \(m\) with respect to \(\left(x_1,y_1\right)\), and it can be arranged as:

\(\displaystyle y-y_1=m\left(x-x_1\right)\)
 
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harpazo

Pure Mathematics
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Mar 20, 2018
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Slope is defined as:

\(\displaystyle m=\frac{\Delta y}{\Delta x}=\frac{y_2-y_1}{x_2-x_1}\)

If we let the second point be the arbitrary point \((x,y)\), we then have:

\(\displaystyle m=\frac{y-y_1}{x-x_1}\)

This gives us the locus of all points that have a slope of \(m\) with respect to \(\left(x_1,y_1\right)\), and it can be arranged as:

\(\displaystyle y-y_1=m\left(x-x_1\right)\)
How often does this formula pop up in calculus 1?
 

MarkFL

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Just about everything you learn before calculus is important.
 

harpazo

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