Lines can be written in the slope-intercept format:

$\displaystyle y=mx+b$

In this format, $\displaystyle m$ equals the line's slope and $\displaystyle b$ represents where the line intercepts the y-axis.

In the given equation:

$\displaystyle m=\frac{7}{9}$

Perpendicular lines have slopes that are negative reciprocals of each other.

First, we need to find its reciprocal.

$\displaystyle \frac{7}{9}\rightarrow\frac{9}{7}$

Second, we need to rewrite it with the opposite sign.

$\displaystyle \frac{9}{7}\rightarrow-\frac{9}{7}$

Only one of the choices has a slope of $\displaystyle -\frac{9}{7}$.

$\displaystyle y=-\frac{9}{7}x+9$ 

Lines can be written in the slope-intercept format:

$\displaystyle y=mx+b$

In this format, $\displaystyle m$ equals the line's slope and $\displaystyle b$ represents where the line intercepts the y-axis.

In the given equation:

$\displaystyle m=\frac{5}{2}$

Perpendicular lines have slopes that are negative reciprocals of each other.

First, we need to find its reciprocal.

$\displaystyle \frac{5}{2}\rightarrow\frac{2}{5}$

Second, we need to rewrite it with the opposite sign.

$\displaystyle \frac{2}{5}\rightarrow-\frac{2}{5}$

Only one of the choices has a slope of $\displaystyle -\frac{2}{5}$.

$\displaystyle y=-\frac{2}{5}x+9$

Lines can be written in the slope-intercept format:

$\displaystyle y=mx+b$

In this format, $\displaystyle m$ equals the line's slope and $\displaystyle b$ represents where the line intercepts the y-axis.

In the given equation:

$\displaystyle m=-\frac{5}{7}$

Perpendicular lines have slopes that are negative reciprocals of each other.

First, we need to find its reciprocal.

$\displaystyle -\frac{5}{7}\rightarrow-\frac{7}{5}$

Second, we need to rewrite it with the opposite sign.

$\displaystyle -\frac{7}{5}\rightarrow\frac{7}{5}$

Only one of the choices has a slope of $\displaystyle \frac{7}{5}$.

$\displaystyle y=\frac{7}{5}x+159$

Lines can be written in the slope-intercept format:

$\displaystyle y=mx+b$

In this format, $\displaystyle m$ equals the line's slope and $\displaystyle b$ represents where the line intercepts the y-axis.

In the given equation:

$\displaystyle m=\frac{3}{4}$

Perpendicular lines have slopes that are negative reciprocals of each other.

First, we need to find its reciprocal.

$\displaystyle \frac{3}{4}\rightarrow\frac{4}{3}$

Second, we need to rewrite it with the opposite sign.

$\displaystyle \frac{4}{3}\rightarrow-\frac{4}{3}$

Only one of the choices has a slope of $\displaystyle -\frac{4}{3}$.

$\displaystyle y=-\frac{4}{3}x+87$ 

Lines can be written in the slope-intercept format:

$\displaystyle y=mx+b$

In this format, $\displaystyle m$ equals the line's slope and $\displaystyle b$ represents where the line intercepts the y-axis.

In the given equation:

$\displaystyle m=2$

Perpendicular lines have slopes that are negative reciprocals of each other.

First, we need to find its reciprocal.

$\displaystyle 2\rightarrow\frac{1}{2}$

Second, we need to rewrite it with the opposite sign.

$\displaystyle \frac{1}{2}\rightarrow-\frac{1}{2}$

Only one of the choices has a slope of $\displaystyle -\frac{1}{2}$.

$\displaystyle y=-\frac{1}{2}x+2$ 

Lines can be written in the slope-intercept format:

$\displaystyle y=mx+b$

In this format, $\displaystyle m$ equals the line's slope and $\displaystyle b$ represents where the line intercepts the y-axis.

In the given equation:

$\displaystyle m=-5$

Perpendicular lines have slopes that are negative reciprocals of each other.

First, we need to find its reciprocal.

$\displaystyle -5\rightarrow-\frac{1}{5}$

Second, we need to rewrite it with the opposite sign.

$\displaystyle -\frac{1}{5}\rightarrow\frac{1}{5}$

Only one of the choices has a slope of $\displaystyle \frac{1}{5}$.

$\displaystyle y=\frac{1}{5}x-5$

Lines can be written in the slope-intercept format:

$\displaystyle y=mx+b$

In this format, $\displaystyle m$ equals the line's slope and $\displaystyle b$ represents where the line intercepts the y-axis.

In the given equation:

$\displaystyle m=\frac{3}{10}$

Perpendicular lines have slopes that are negative reciprocals of each other.

First, we need to find its reciprocal.

$\displaystyle \frac{3}{10}\rightarrow\frac{10}{3}$

Second, we need to rewrite it with the opposite sign.

$\displaystyle \frac{10}{3}\rightarrow-\frac{10}{3}$

Only one of the choices has a slope of $\displaystyle -\frac{10}{3}$.

$\displaystyle y=-\frac{10}{3}x+98$ 

Lines can be written in the slope-intercept format:

$\displaystyle y=mx+b$

In this format, $\displaystyle m$ equals the line's slope and $\displaystyle b$ represents where the line intercepts the y-axis.

In the given equation:

$\displaystyle m=100$

Perpendicular lines have slopes that are negative reciprocals of each other.

First, we need to find its reciprocal.

$\displaystyle 100\rightarrow\frac{1}{100}$

Second, we need to rewrite it with the opposite sign.

$\displaystyle \frac{1}{100}\rightarrow-\frac{1}{100}$

Only one of the choices has a slope of $\displaystyle -\frac{1}{100}$.

$\displaystyle y=-\frac{1}{100}x+85$ 

Write the perpendicular line slope formula.  The perpendicular slope is the negative reciprocal of the original slope.

$\displaystyle m_{perpendicular} = -\frac{1}{m_{original}}$

Let $\displaystyle y=2x$ be the original equation.  The slope is $\displaystyle 2$.  Substitute this into the equation to find the slope of any perpendicular line.

$\displaystyle m_{perpendicular} = -\frac{1}{2}$

The slope of a perpendicular line must have a slope of $\displaystyle -\frac{1}{2}$, which is also the slope for $\displaystyle y= -\frac{1}{2}x$.

The answer is:

$\displaystyle \textup{Yes, the slopes are negative reciprocal to each other.}$

Lines are perpendicular if their slopes are negative reciprocals of one another. For example, the negative reciprocal of $\displaystyle 3=-\frac{1}{3}$. So  $\displaystyle y=-2x+3$ is perpendicular to $\displaystyle y=\frac{1}{2}x-4$ because their slopes are the negative reciprocals of each other. $\displaystyle \frac{1}{2}=-2\hspace{1mm}and\hspace{1mm} -2=-\frac{1}{-2}=\frac{1}{2}$.  A positive slope can still be the negative reciprocal as you can see.