What is the equation of the line passing through $(3, 4)$ $(3,4)$ and $(9, 19)$ $(9,19)$ ?

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Answer 1 · 2015-11-18T02:52:28

$y = \frac{5}{2} x - \frac{7}{2}$ $y = 5/2x - 7/2$

First, get the slope

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

$\Rightarrow m = \frac{4 - 19}{3 - 9}$ $=> m = (4 - 19)/(3 - 9)$

$\Rightarrow m = - \frac{15}{- 6}$ $=> m = -15/-6$

$\Rightarrow m = \frac{5}{2}$ $=> m = 5/2$

Next, get the $y$ $y$ -intercept. We do this by plugging-in any of the given points

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

$\Rightarrow 4 = \frac{5}{2} (3) + b$ $=> 4 = 5/2(3) + b$

$\Rightarrow 4 = \frac{15}{2} + b$ $=> 4 = 15/2 + b$

$\Rightarrow b = 4 - \frac{15}{2}$ $=> b = 4 - 15/2$

$\Rightarrow b = \frac{8 - 15}{2}$ $=> b = (8 - 15)/2$

$\Rightarrow b = - \frac{7}{2}$ $=> b = -7/2$

Hence, the equation of the line passing through the points $(3, 4)$ $(3, 4)$ and $(9, 19)$ $(9, 19)$ is

$y = \frac{5}{2} x - \frac{7}{2}$ $y = 5/2x - 7/2$

What is the equation of the line passing through (3,4)(3,4)(3,4) and (9,19)(9,19)(9,19)?