Question

Line g passes through points (1, 1) and (10, 9). Line h is perpendicular to g. What is the
slope of line h?

Answer 1

Answer:

$\bold{The~slope~of~line~h~is~-\frac{9}{8}. }$

Step-by-step explanation:

Hi there!

First, let's calculate the slope of line g.

$\displaystyle\frac{y2-y1}{x2-x1}$

$\displaystyle\frac{9-1}{10-1} \\ \displaystyle\frac{8}{9}$

So, the slope of line g is $\displaystyle\frac{8}{9}$

Now let's identify the slope of line h.

We are given that line h is perpendicular to line g.

Now, perpendicular lines have slopes that are opposite reciprocals.

This means we take a number, flop it over, and change its sign.

The slope of line g is

$\displaystyle\frac{8}{9}$

Now, we flop it over:

$\displaystyle\frac{9}{8}$

Then, we change its sign:

$\displaystyle-\frac{9}{8}$

Thus, $\displaystyle-\frac{9}{8}$ is our final answer.

Hope it helps! Enjoy your day! (:

$\bold{GazingAtTheStars}$