# What is the equation of the line perpendicular to y=-3/7x  that passes through  (5,7) ?

Dec 13, 2015

$y = \frac{3}{7} x + \frac{34}{7}$

#### Explanation:

So, the line we need to determine is $\text{perpendicular}$ to the given line. Thus, the slope is the $\text{negative reciprocal}$ of the slope of the line given.

Since the line given is in $\text{slope-intercept form}$, we can easily find the slope as it will be the constant being multiplied to the $x$ term. In this line, it will be $- \frac{3}{7}$.

Then, we calculate the $\text{negative reciprocal}$ of it. First negating it, we get $\frac{3}{7}$. Then, taking the reciprocal, it will be $\frac{7}{3}$.

Now, we have our slope of our new line. We are also given a point, so we can use $\text{point-slope formula}$ to determine our new line.

Doing so yields:

$\left(y - 7\right) = \frac{3}{7} \left(x - 5\right)$

Now, this is an acceptable form of a line. But since the question gives you a line in $\text{slope-intercept}$ form, you should give your answer in that form as well.

Converting this line to slope intercept, we get:

$y - 7 = \frac{3}{7} x - \frac{15}{7}$

$y = \frac{3}{7} x - \frac{15}{7} + \frac{49}{7}$

$y = \frac{3}{7} x + \frac{34}{7}$