Question

Consider the line 2x +5y = -2.(a) What is the slope of a line parallel to this line?(b) What is the slope of a line perpendicular to this line?

Answer 1

ANSWER:

(a) Parallel slope = -2/5

(b) Perpendicular slope = 5/2

STEP-BY-STEP EXPLANATION:

We have the following equation:

$2x+5y=-2$

To determine the slope, we solve for y, like so:

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

The slope is the quotient of x, so the slope of the line is -2/5

(a)

When two lines are parallel the slope is the same.

Therefore :

m = -2/5

(b)

Now, when the lines are perpendicular, the product of both slopes is equal to -1, just like this:

$\begin{gathered} m_1\cdot m_2=-1 \\ -\frac{2}{5}\cdot m_2=-1 \\ m_2=\frac{5}{2} \end{gathered}$

(a) Parallel slope = -2/5

(b) Perpendicular slope = 5/2