Which of the following equations is perpendicular to the given function:

To find a line perpendicular to a given linear function, simply find the opposit reciprocal of the slope of the given function.

So, we begin with 4, the opposite reciprocal will have the opposite sign and will be the flipped fraction of 4, so it will look like this:

So we need to choose the answer with the correct slope, choose the only option with slope:

Two perpendicular lines have slopes that are opposite reciprocals, meaning that the sign changes and the reciprocal of the slope is taken.

The original equation is in slope-intercept form,

where represents the slope.

In this case, the slope of the original is:

After taking the opposite reciprocal, the result is the slope below:

The line is a vertical line. Therefore, a perpendicular line is going to be horizontal and have a slope of zero.

The equation is such a line.

The lines and are both vertical lines, while the lines and have slopes of and , respectively.

Two lines are perpendicular if and only if the product of their slopes is . The slope of each line can be found from the coordinates of two points using the slope formula

To find the slope of the first line, set :

To find the slope of the second line, set :

The product of the slopes is

As the product is not , the lines are not perpendicular.

Two lines on the coordinate plane are perpendicular if and only if the product of their slopes is . The product of the slopes of the lines in question is

,

so the lines are indeed perpendicular.

Lines can be written in the slope-intercept format:

In this format, equals the line's slope and represents where the line intercepts the y-axis.

In the given equation:

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

First, we need to find its reciprocal.

Rewrite.

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

Only one of the choices has a slope of .

Two lines are perpendicular if their slopes are opposite reciprocals of each other (opposite: different signs, reciprocal: numerator and denominator are switched).

To find the slopes, we will write the original equation in slope-intercept form

where m is the slope. Given the original equation

we must solve for y. To do that, we will divide each term by -9. We get

Therefore, the slope of this line is -6. We must find a line that has a slope that is the opposite reciprocal of this line. The opposite reciprocal slope of -6 is .

Let's look at the line

We must write it in slope-intercept form. To do that, we will divide each term by 12. We get

We can simplify to

The slope of this line is . Therefore, it is perpendicular to the original line.

Two lines are perpendicular if they have slopes that are opposite reciprocals of each other (opposite: different signs, reciprocal: switch the numerator and denominator).

To find the slope of a line, we write it in slope-intercept form

where m is the slope.

Given the equation

we will solve for y by dividing each term by -3.

We can see that the slope of this line is 3. The slope of a line perpendicular to this one will have a slope of .

Therefore, the line

is perpendicular to the original line.

The only marker for whether lines are perpendicular is whether their slopes are the opposite-reciprocal for the other line's slope. The -intercept is not important. Therefore, the line perpendicular to will have a slope of or

Lines can be written in the slope-intercept format:

In this format, equals the line's slope and represents where the line intercepts the y-axis.

In the given equation:

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

First, we need to find its reciprocal.

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

Only one of the choices has a slope of .