Question

Find the slope of a line that is perpendicular to the line 10x + 5y = 10. Round your answer to the nearest hundredth, if necessary.

Answer 1

The line

$10x+5y=10$

Can be written as:

$\begin{gathered} 10x+5y=10 \\ 5y=-10x+10 \\ y=-\frac{10}{5}x+\frac{10}{5} \\ y=-2x+2 \end{gathered}$

This is the same line in the slope-intercept form:

$y=mx+b$

Then, the original line has an slope of -2.

To find the slope of a perpendicular line to this one we need to remmeber that two lines are perpendicular if and only if

$m_1m_2=-1_{}_{}$

Plugging the value of the original line we have:

$\begin{gathered} -2m_2=-1 \\ m_2=-\frac{1}{-2} \\ m_2=\frac{1}{2} \end{gathered}$

Therefore a line perpendicular to the line 10x+5y=10 has slope 1/2 or 0.5.