Algebra - How to find out if lines are perpendicular

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

$y=\frac{-1}{4}x+365$

$y=\frac{1}{4}x+17$

$y=\frac{-1}{2}x+35$

Explanation

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:

$\frac{-1}{4}$

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

$\frac{-1}{4}$

Which of the following equations describes a line perpendicular to the line ?

$x=\frac{1}{3}$

$x=-\frac{1}{3}$

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

Explanation

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 $x=\frac{1}{3}$ and $x=-\frac{1}{3}$ are both vertical lines, while the lines and $y=-\frac{x}{3}$ have slopes of and $-\frac{1}{3}$ , respectively.

Find the line that is perpendicular to

$y = -\frac{1}{3}x - 1$

$y = \frac{1}{3}x - 2$

$y = \frac{1}{9}x + 4$

Explanation

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.

$\frac{-3y}{-3} = \frac{-9x}{-3} + \frac{12}{-3}$

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 $-\frac{1}{3}$ .

Therefore, the line

$y = -\frac{1}{3}x - 1$

is perpendicular to the original line.

Find a line perpendicular to the line with the equation:

$y=\frac{1}{2}x+79$

$y=\frac{1}{2}x-10$

$y=-\frac{1}{2}x-10$

Explanation

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:

$m=\frac{1}{2}$

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

First, we need to find its reciprocal.

$\frac{1}{2}\rightarrow\frac{2}{1}$

Rewrite.

$\frac{2}{1}=2$

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

$2\rightarrow-2$

Only one of the choices has a slope of .

Which of the following lines could be perpendicular to the following:

$y=\frac{3}{4}x-2$

$y=-1\frac{1}{3}x-128$

$y=\frac{3}{4}x+2$

$y=\frac{4}{6}x-17$

None of the available answers

Explanation

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 $y=\frac{3}{4}x-2$ will have a slope of $m=-\frac{4}{3}$ or $m=-1\frac{1}{3}$

Find the line that is perpendicular to the following:

Explanation

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

$\frac{-9y}{-9} = \frac{54x}{-9} + \frac{27}{-9}$

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 $\frac{1}{6}$ .

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

$\frac{12y}{12} = \frac{2x}{12} + \frac{1}{12}$

$y = \frac{2}{12}x + \frac{1}{12}$

We can simplify to

$y = \frac{1}{6}x + \frac{1}{12}$

The slope of this line is $\frac{1}{6}$ . Therefore, it is perpendicular to the original line.

Find a line perpendicular to the line with the equation:

$y=\frac{7}{9}x-1$

$y=-\frac{9}{7}x+9$

$y=\frac{7}{9}x+6$

$y=-\frac{7}{9}x-8$

$y=\frac{9}{7}x+15$

Explanation

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:

$m=\frac{7}{9}$

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

First, we need to find its reciprocal.

$\frac{7}{9}\rightarrow\frac{9}{7}$

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

$\frac{9}{7}\rightarrow-\frac{9}{7}$

Only one of the choices has a slope of $-\frac{9}{7}$ .

$y=-\frac{9}{7}x+9$

Which of these lines is perpendicular to

$4y-2x=12\ ?$

$y=\frac{1}{2}x-8$

$y=-\frac{1}{2}x+6$

None of the other answers

Explanation

Perpendicular lines have slopes that are negative reciprocals of each other. If you convert the given line to the form, you get

$y=\frac{1}{2}x+3$

which indicates a slope of $\frac{1}{2}$ . Thus, the slope of the perpendicular line must be , which is the negative reciprocal of $\frac{1}{2}$ . The only line with a slope of is

Which of these lines is perpendicular to ?

$y=\frac{1}{3}x-9$

$y=-\frac{1}{3}x-7$

Explanation

Perpendicular lines have slopes that are negative reciprocals of one another. Since all of these lines are in the format, it is easy to determine their slopes, or .