# Write an equation perpendicular to the given line through the given point

This is the slope intercept form. The reference slope is. These two lines are perpendicular, but the product of their slopes is not —1. It was left up to the student to figure out which tools might be handy. Now I need a point through which to put my perpendicular line.

### Write an equation perpendicular to the given line through the given point

The reference slope is. Pictures can only give you a rough idea of what is going on. So the lines formed by all of the following functions will be parallel to f x. Then the perpendicular slope is. 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! Instead of using the same slope, however, we use the negative reciprocal of the given slope. It'll cross where the two lines' equations are equal, so I'll set the non-y sides of the second original line's equaton and the perpendicular line's equation equal to each other, and solve: The above more than finishes the line-equation portion of the exercise.

Write the equation for the line. With this point and my perpendicular slope, I can find the equation of the perpendicular line that'll give me the distance between the two original lines: Okay; now I have the equation of the perpendicular.

How To: Given the equation of a function and a point through which its graph passes, write the equation of a line parallel to the given line that passes through the given point. Ah; but I can pick any point on one of the lines, and then find the perpendicular line through that point. Please accept "preferences" cookies in order to enable this widget. Parallel, Perpendicular Lines Purplemath There is one other consideration for straight-line equations: finding parallel and perpendicular lines. As long as you can convert a linear equation to slope intercept form, you can easily determine the slope of the line, and since the slope of a perpendicular line is the negative reciprocal, you can determine that as well.

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

Analysis of the Solution We can confirm that the two lines are parallel by graphing them. So I'll use the point-slope form to find the line: This is the parallel line that they'd asked for, and it's in the slope-intercept form that they'd specified. Write the equation for the line. Instead of using the same slope, however, we use the negative reciprocal of the given slope. Any other line with a slope of 3 will be parallel to f x. Affiliate Now I need to find two new slopes, and use them with the point they've given me; namely, with the point 4, —1. In other words, they're asking me for the perpendicular slope, but they've disguised their purpose a bit. If you know the equation of the line in standard form, you simply need to divide the coefficient of the y term by the coefficient of the x term to find the slope of a perpendicular line. Writing Equations of Parallel Lines Suppose for example, we are given the following equation. This is just my personal preference. Analysis of the Solution A graph of the two lines is shown in Figure Hey, now I have a point and a slope! Where does this line cross the second of the given lines? This would give you your second point.

Then I can find where the perpendicular line and the second line intersect.

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