How do I find the slope of a perpendicular line to a given linear equation?

Question

First, let's find the slope of the original equation:

The slope of the line y=2/3x+5 is 2/3.

Now, let's find the reciprocal of that slope:

The reciprocal of 2/3 is 3/2.

The numerator of the fraction became the denominator, and the denominator became the numerator.

Next, we "negate" or take the opposite of the reciprocal:

The opposite of 3/2 is -3/2.

Notice that 3/2 was positive, so all we had to do was add a negative sign. This is essentially multiplying the number by a negative 1.

If it had been negative, we would need to make it positive. This can also be done by multiplying the negative number by a negative 1, making the number positive.

We are finished! The slope of a perpendicular line to y=2/3x+5 is -3/2.

Here are more examples:

The slope of a perpendicular line to y=-1/2x+3 is 2/1 or just 2.

The slope of a perpendicular line to y=5x+4 is -1/5.

The slope of a perpendicular line to y=x+2 is -1. This is true because "x" is always multiplied by 1 when it has no number beside it, and the reciprocal of 1 (1/1) is 1. If I wrote the equation for a line perpendicular to y=x+2 it might look like y=-x+4. Notice you only need to write the negative sign beside the "x".

Great work expanding your math knowledge today! You can do this! :)

Answer 1

Sometimes, your given problems that look like this:

"Find the slope that is perpendicular to the line y = (-1/3)x + (1/2)."

To do this, you have to find the slope of the line that you already have. m = -1/3

Next, you take the "opposite reciprocal." When I am teaching a class, I will tell my students to "FLIP IT and SWITCH IT." So, our slope was m = -1/3, so the perpendicular slope would be m = 3

SOLUTION: m = 3

Answer 2

First, let's find the slope of the original equation:

The slope of the line y=2/3x+5 is 2/3.

Now, let's find the reciprocal of that slope:

The reciprocal of 2/3 is 3/2.

The numerator of the fraction became the denominator, and the denominator became the numerator.

Next, we "negate" or take the opposite of the reciprocal:

The opposite of 3/2 is -3/2.

Notice that 3/2 was positive, so all we had to do was add a negative sign. This is essentially multiplying the number by a negative 1.

If it had been negative, we would need to make it positive. This can also be done by multiplying the negative number by a negative 1, making the number positive.

We are finished! The slope of a perpendicular line to y=2/3x+5 is -3/2.

Here are more examples:

The slope of a perpendicular line to y=-1/2x+3 is 2/1 or just 2.

The slope of a perpendicular line to y=5x+4 is -1/5.

The slope of a perpendicular line to y=x+2 is -1. This is true because "x" is always multiplied by 1 when it has no number beside it, and the reciprocal of 1 (1/1) is 1. If I wrote the equation for a line perpendicular to y=x+2 it might look like y=-x+4. Notice you only need to write the negative sign beside the "x".

Great work expanding your math knowledge today! You can do this! :)