What is the equation of the line between $(12, 23)$ $(12,23)$ and $(9, 14)$ $(9,14)$ ?

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Answer 1 · 2018-06-05T17:02:57

$y = 3 x - 13$ $y=3x-13$

$(12, 23) and (9, 14)$ $(12,23) and (9,14)$

First use the definition of slope:

$m = \frac{y_{2} - y_{1}}{x_{2} - x_{1}}$ $m=(y_2-y_1)/(x_2-x_1)$

$m = \frac{14 - 23}{9 - 12} = 3$ $m=(14-23)/(9-12) = 3$

Now use the point slope form of a line with either point:

$y - y_{1} = m (x - x_{1})$ $y-y_1=m(x-x_1)$

$y - 23 = 3 (x - 12)$ $y-23=3(x-12)$

This is a valid solution, if you like you can do the algebra to convert to slope intercept form:

$y = 3 x - 13$ $y=3x-13$

graph{y=3x-13 [-20.34, 19.66, -16.44, 3.56]}

What is the equation of the line between (12,23)(12,23)(12,23) and (9,14)(9,14)(9,14)?