How do you write the equation of a line in point slope form and slope intercept form given points (2, 7) (1, -4)?

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Answer 1 · 2015-05-23T22:49:57

The slope of the line segment between two points is the change in $y$ divide by the change in $x$ .

For the case of a line through $(2,7)$ and $(1,-4)$ we have

slope $m = (Delta y)/(Delta x) = (-4-7)/(1-2) = -11/-1 = 11$

Using the point $(2,7)$ we can write the equation of the line in point slope form as:

$y-7 = m(x - 2)$ where the slope $m = 11$ .

That is:

$y - 7 = 11(x - 2)$

To get point intercept form, first expand the right hand side so...

$y - 7 = 11x - (11*2) = 11x - 22$

Then add $7$ to both sides to get:

$y = 11x - 15 = 11x + (-15)$

This is point intercept ( $y = mx+c$ ) form with slope $m = 11$ and intercept $c = -15$ .