# How do you write an equation of a line given point (3,7) and slope 2/7?

Apr 30, 2018

$y = \frac{2}{7} x + \frac{43}{7}$

#### Explanation:

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

•color(white)(x)y=mx+b

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

$\text{here } m = \frac{2}{7}$

$\Rightarrow y = \frac{2}{7} x + b \leftarrow \textcolor{b l u e}{\text{is the partial equation}}$

$\text{to find b substitute "(3,7)" into the partial equation}$

$7 = \frac{6}{7} + b \Rightarrow b = \frac{49}{7} - \frac{6}{7} = \frac{43}{7}$

$\Rightarrow y = \frac{2}{7} x + \frac{43}{7} \leftarrow \textcolor{red}{\text{equation of line}}$

Apr 30, 2018

$y = \frac{2 x}{7} + \frac{43}{7}$ (form: y = mx + c)

$2 x - 7 y + 43 = 0$ (form: ax + by + c = 0)

Either are acceptable answers. Your teacher may prefer a certain form.

#### Explanation:

By the Point-Slope Form, (which, by the way, is a method of computing the equation of a line given its slope and a point on it):

$\left(y - {y}_{1}\right) = m \left(x - {x}_{1}\right)$ where $m$ is the slope and $\left({x}_{1} , {y}_{1}\right)$ is the coordinates of the given point.
$\left(y - 7\right) = \frac{2}{7} \left(x - 3\right)$
$\left(y - 7\right) = \frac{2 x}{7} - \frac{6}{7}$
$y = \frac{2 x}{7} + \frac{43}{7}$