# How to write an equation perpendicular to a line

### Perpendicular lines slope

Slope of the parallel line: Since parallel lines have the same slope, what do you think the slope of the parallel line is going to be? If you said -7, you are correct!!! Don't be afraid of exercises like this. What are the two things we need to write an equation of a line???? The reference slope is. Now we can use the point to find the y-intercept by substituting the given values into the slope-intercept form of a line and solving for b. OK, now we have our slope, which is 4. Analysis of the Solution We can confirm that the two lines are parallel by graphing them. It is a horizontal line. We need to do a little digging to get our slope.

Find the slope of the function. But even just trying them, rather than immediately throwing your hands up in defeat, will strengthen your skills — as well as winning you some major "brownie points" with your instructor.

Figure 22 Writing Equations of Perpendicular Lines We can use a very similar process to write the equation for a line perpendicular to a given line. Don't be afraid of exercises like this.

So, if we know the slope of the line parallel to our line, we have it made. Otherwise, they must meet at some point, at which point the distance between the lines would obviously be zero.

### Find the equation of the line that is perpendicular to this line and passes through the point

OK, now we have our slope, which is 4. The perpendicular slope being the value of "a" for which they've asked me will be the negative reciprocal of the reference slope. Analysis of the Solution We can confirm that the two lines are parallel by graphing them. Solve for b. Are these lines parallel? Of greater importance, notice that this exercise nowhere said anything about parallel or perpendicular lines, nor directed us to find any line's equation. These two lines are perpendicular, but the product of their slopes is not —1. Pictures can only give you a rough idea of what is going on. If you need a review on vertical lines, feel free to go to Tutorial Graphing Lines. Perpendicular Lines and Their Slopes In other words, perpendicular slopes are negative reciprocals of each other. Slope of the parallel line: Since parallel lines have the same slope what do you think the slope of the parallel line is going to be?

Then the full solution to this exercise is: parallel: perpendicular: Warning: If a question asks you whether two given lines are "parallel, perpendicular, or neither", you must answer that question by finding their slopes, not by drawing a picture! I'll first need to find the slope of the reference line.

If you said 0, you are right on. This one is a little trickier.

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