# What is the equation of the line between (12,7) and (9,14)?

$7 x + 3 y - 105 = 0$

#### Explanation:

The equation of the line passing through the points $\left({x}_{1} , {y}_{1}\right) \setminus \equiv \left(12 , 7\right)$ & $\left({x}_{2} , {y}_{2}\right) \setminus \equiv \left(9 , 14\right)$ is given by following formula

$y - {y}_{1} = \setminus \frac{{y}_{2} - {y}_{1}}{{x}_{2} - {x}_{1}} \left(x - {x}_{1}\right)$

$y - 7 = \setminus \frac{14 - 7}{9 - 12} \left(x - 12\right)$

$y - 7 = - \setminus \frac{7}{3} \left(x - 12\right)$

$3 y - 21 = - 7 x + 84$

$7 x + 3 y - 21 - 84 = 0$

$7 x + 3 y - 105 = 0$

Jul 27, 2018

$y = - \frac{7}{3} x + 35$

#### Explanation:

$\text{the equation of a line in "color(blue)"slope-intercept form}$ is.

•color(white)(x)y=mx+c

$\text{where m is the slope and c the y-intercept}$

$\text{to calculate m use the "color(blue)"gradient formula}$

•color(white)(x)m=(y_2-y_1)/(x_2-x_1)

$\text{let "(x_1,y_1)=(12,7)" and } \left({x}_{2} , {y}_{2}\right) = \left(9 , 14\right)$

$m = \frac{14 - 7}{9 - 12} = \frac{7}{- 3} = - \frac{7}{3}$

$y = - \frac{7}{3} x + c \leftarrow \textcolor{b l u e}{\text{is the partial equation}}$

$\text{to find c substitute either of the 2 given points into}$
$\text{the partial equation}$

$\text{using "(12,7)" then}$

$7 = - 28 + c \Rightarrow c = 7 + 28 = 35$

$y = - \frac{7}{3} x + 35 \leftarrow \textcolor{b l u e}{\text{equation in slope-intercept form}}$