How do you write an equation in slope intercept form of a line containing the coordinates (10,-12) and (13,18)?

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Answer 1 · 2016-04-27T11:53:36

$y = 10 x - 112$ $y=10x-112$

We start with the points:

$(10, - 12); (13, 18)$ $(10,-12); (13,18)$

We are trying to get the equation in the form

$y = m x + b$ $y=mx+b$

where $m$ $m$ is the slope which we calculate using the rise over the run:

$m = \frac{- 12 - 18}{10 - 13} = - \frac{30}{- 3} = 10$ $m =( -12-18)/(10-13) = -30/-3 = 10$

so the equation becomes

$y = 10 x + b$ $y=10x+b$

We can determine the y-intercept, $b$ $b$ , by substituting either known point into this equation - let's use the point $(10, - 12)$ $(10,-12)$

$- 12 = 100 + b \Rightarrow b = - 112$ $-12=100+b implies b=-112$

We can now graph the equation:

$y = 10 x - 112$ $y=10x-112$

graph{(y-10*x+112)=0 [-60, 60, -19, 21]}