Question

Consider the line – 5x – 8y= 3.
What is the slope of a line perpendicular to this line?
What is the slope of a line parallel to this line?

Answer 1

Answer:

Perpendicular Slope: 8/5

Parallel Slope: -5/8

Step-by-step explanation:

First, let's rewrite the line into slope intercept form.

-5x - 8y = 3

-8y = 5x + 3

y = -5x/8 + -3/8

Okay, so now we know the slope, -5/8, and the y-intercept, -3/8.

For a line to be perpendicular, the slope needs to be opposite of the given line's slope.  This will cause the two lines to cross at a 90-degree angle, and therefore be perpendicular.

So a perpendicular line could be as follows:

y = 8x/5 + -3/8

So the perpendicular slope would be 8/5.

For a line to be parallel, the slope needs to be the same so that the two lines will never cross.

So a parallel line could be as follows:

y = -5x/8 + 1

So the parallel slope would be -5/8.

Cheers.

Answer 2

Answer:

Perpendicular Slope: $\boxed{\frac{8}{5}}$

Parallel Slope: $\boxed{-\frac{5}{8}}$

Step-by-step explanation:

Part 1: Rewrite into slope-intercept form

Firstly, the equations are written in standard form and not slope-intercept form, so to change that, follow the steps below.

Note: Remember the slope-intercept form equation - $\boxed{y=mx+b}$

$-5x-8y=3\\\\5x + (-5x-8y)=3+5x\\\\-8y=5x+3\\\\\frac{-8y}{-8} =\frac{5x+3}{-8}$

$y=-\frac{5}{8}x-\frac{3}{8}$

Add $5x$ to both sides of the equation to isolate the y-variable. Then, divide by the coefficient of y to isolate it entirely. The equation is now in slope-intercept form.

Part 2: Determine the perpendicular slope

Perpendicular slopes are reciprocals of the given slopes. To turn the original slope into its reciprocal counterpart, follow these steps:

1. If the current slope is positive, add a negative sign. If the current slope is negative, remove the negative sign.
2. The denominator becomes the numerator and the numerator becomes the denominator.

To follow this for the slope of the given equation:

$\boxed{-\frac{5}{8} \dashrightarrow \frac{8}{5} }$

Part 3: Determine the parallel slope

Parallel slopes are equal - otherwise, the lines would eventually intersect. Therefore, the given slope is also the parallel slope.

The parallel slope is $\boxed{-\frac{5}{8}}$.