What is the equation of the line passing through $(18, 23), (12, 8)$ $(18,23), (12,8)$ ?

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What is the equation of the line passing through $(18, 23), (12, 8)$ $(18,23), (12,8)$ ?

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Answer 1 · 2018-04-18T19:21:50

$y = \frac{5}{2} x - 22$ $y=5/2x-22$

Explanation:

$the equation of a line in point-slope form$ $"the equation of a line in "color(blue)"point-slope form"$ is.

$∙ x y = m x + b$ $•color(white)(x)y=mx+b$

$where m is the slope and b the y-intercept$ $"where m is the slope and b the y-intercept"$

$to calculate m use the gradient formula$ $"to calculate m use the "color(blue)"gradient formula"$

$∙ x m = \frac{y_{2} - y_{1}}{x_{2} - x_{1}}$ $•color(white)(x)m=(y_2-y_1)/(x_2-x_1)$

$let (x_{1}, y_{1}) = (18, 23) and (x_{2}, y_{2}) = (12, 8)$ $"let "(x_1,y_1)=(18,23)" and "(x_2,y_2)=(12,8)$

$\Rightarrow m = \frac{8 - 23}{12 - 18} = \frac{- 15}{- 6} = \frac{5}{2}$ $rArrm=(8-23)/(12-18)=(-15)/(-6)=5/2$

$\Rightarrow y = \frac{5}{2} x + b \leftarrow is the partial equation$ $rArry=5/2x+blarrcolor(blue)"is the partial equation"$

$to find b substitute either of the 2 given points into$ $"to find b substitute either of the 2 given points into"$
$the partial equation$ $"the partial equation"$

$using (12, 8) then$ $"using "(12,8)" then"$

$8 = 30 + b \Rightarrow b = 8 - 30 = - 22$ $8=30+brArrb=8-30=-22$

$\Rightarrow y = \frac{5}{2} x - 22 \leftarrow is the equation$ $rArry=5/2x-22larrcolor(red)"is the equation"$

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What is the equation of the line passing through $(18, 23), (12, 8)$ $(18,23), (12,8)$ ?

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What is the equation of the line passing through $(18, 23), (12, 8)$ $(18,23), (12,8)$ ?