How to find the equation of a perpendicular line

Perpendicular lines have slopes that are opposite reciprocals meaning that the slope is flpped. The equation that satisfies both of these criteria is:

A line is perpendicular to another line when they meet at a degree angle. That angle is the result of the slopes of the lines being opposite reciprocals.

The "opposite reciprocal" of is best described as .

First we reorganize the original equation to isolate . To do this we want to get our equation into slope intercept form .

First subtract 12 from each side.

Now divide by 4 and simplify where possible.

opposite reciprocal

The only equation in the answer choices with a slope of is

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When finding the slope of a perpendicular line, we need to ensure we have form. stands for slope. Our is . To find the perpendicular slope, we need to take the negative reciprocal of that value which is . Since we are looking for an equation, we need to reuse the form to solve for . We do this by plugging in our coordinates.

Add on both sides.

Our equation is now .

Step 1: get the line into y = mx +b format to find the slope m:

Next, we need to remember that perpendicular lines have slopes that are negative reciprocals. Find the negative reciprocal of :

Perpendicular lines have slopes that are negative reciprocals of each other. The given line has a slope of . The negative reciprocal of is , so the perpendicular line must have a slope of . The only line with a slope of is .

When finding the slope of a perpendicular line, we need to ensure we have form. Let's rearrange it. By subtracting on both sides and dividing on both sides, we get . stands for slope. Our is . To find the perpendicular slope, we need to take the negative reciprocal of that value which is . Since we are looking for an equation, we need to reuse the form to solve for . We do this by plugging in our coordinates.

Subtract on both sides.

Our equation is now .

To find the equation of a line, we need to know the slope and a point that passes through the line. Once we know this, we can use the equation where m is the slope of the line, and is a point on the line. For perpendicular lines, the slopes are negative reciprocals of each other. The slope of is 5, so the slope of the perpendicular line will have a slope of . We know that the perpendicular line needs to contain the point (5,3), so we have all of the information we need. We can now use the equation

When finding the slope of a perpendicular line, we need to ensure we have form. Let's rearrange it. By add on both sides and dividing on both sides, we get . stands for slope. Our is . To find the perpendicular slope, we need to take the negative reciprocal of that value which is . Since we are looking for an equation, we need to reuse the form to solve for . We do this by plugging in our coordinates.

Add on both sides.

Our equation is now .

The slope must be the negative reciprocal and the line must pass through the point (3,2). So the slope becomes and this is plugged into to solve for the -intercept.

Two lines are perpendicular if and only if their slopes are "negative reciprocals" of each other such as 1/2 and -2. In our problem we are not given line equations that we can readily see the slope, so we must convert each equation to slope intercept form or .

First find out the slope of the given equation by converting it to slope-intercept form:

So we need a line whose slope is the negative reciprocal of -1/8 (which is 8). Even though this number is not "negative" the idea of the negative reicprocal gives a positive number here because two negative signs cancel each other to make a positive. ...negative recicprocal....

Now we must choose an equation that, after being changed to slope intercept form has a slope of 8.

So (answer) is the equation of a line that is perpendicular to

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