# What is the equation of the line perpendicular to y=2/7x  that passes through  (-2,9) ?

May 7, 2018

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

#### Explanation:

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

•color(white)(x)y=mx+b

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

$y = \frac{2}{7} x \text{ is in this form}$

$\text{with slope m "=2/7" and } b = 0$

$\text{given the equation of a line with slope m then the }$
$\text{equation of a line perpendicular to it is}$

•color(white)(x)m_(color(red)"perpendicular")=-1/m

$\Rightarrow {m}_{\text{perpendicular}} = - \frac{1}{\frac{2}{7}} = - \frac{7}{2}$

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

$\text{to find b substitute "(-2,9)" into the partial equation}$

$9 = 7 + b \Rightarrow b = 9 - 7 = 2$

$\Rightarrow y = - \frac{7}{2} x + 2 \leftarrow \textcolor{red}{\text{perpendicular equation}}$

May 7, 2018

See details below

#### Explanation:

The general equation of a stright line is $y = m x + n$

where m is the slope and n is y-intercept

We know also that if m is the slope, then $- \frac{1}{m}$ is the slope of perpendicular line to the line given. In our case, we have

$m = \frac{2}{7}$, and $n = 0$ then the slope of perpendicular is $m ' = - \frac{7}{2}$

The reuqested equation is $y = - \frac{7}{2} x + n$

We dont know what is the n value, but they asking for a line perpendicular passing thru $\left(- 2 , 9\right)$, Then this point acomplish the line equation. That means 9=-7/2·(-2)+n

Transposing terms we found $n = 2$. Finally the equation is

$y = - \frac{7}{2} x + 2$
See graph below (A is the given point) 