## 17Calculus Precalculus - Perpendicular Lines

##### 17Calculus

Perpendicular Lines

In the case of perpendicular lines, if the equation of one line is $$y = mx + b_1$$, the equation of the other is $$y=-x/m+b_2$$ So the slope of the second line is said to be the negative reciprocal of the first line.

Be careful here. There is a tendency to think that if you are given the equation of the first line as $$y = mx + b_1$$, to get the equation of ANY perpendicular line you just replace the slope with the negative reciprocal, i.e. $$m \to -1/m$$. However, this doesn't work in all cases since the y-intercept will most likely be different. So you need to take into account that $$b_1 \neq b_2$$ most of the time and you need calculate $$b_2$$. Working practice problems will help you understand this.

Practice

Unless otherwise instructed, find the equation of the line, in slope-intercept form, perpendicular to the given line going through the given point.

line: $$9x+12y=2$$ point: $$(15,7)$$

Problem Statement

Find the equation of the line, in slope-intercept form, perpendicular to $$9x+12y=2$$ containing the point $$(15,7)$$.

$$y=4x/3 - 13$$

Problem Statement

Find the equation of the line, in slope-intercept form, perpendicular to $$9x+12y=2$$ containing the point $$(15,7)$$.

Solution

### 2728 video solution

$$y=4x/3 - 13$$

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line: $$10x+2y=9$$ point: $$(20,3)$$

Problem Statement

Find the equation of the line, in slope-intercept form, perpendicular to $$10x+2y=9$$ going through the point $$(20,3)$$.

$$y = x/5 - 1$$

Problem Statement

Find the equation of the line, in slope-intercept form, perpendicular to $$10x+2y=9$$ going through the point $$(20,3)$$.

Solution

### 2729 video solution

$$y = x/5 - 1$$

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line: $$x - 4y = 15$$ point: $$(3, 1)$$

Problem Statement

Determine the equation of the line that is perpendicular to $$x - 4y = 15$$ and passes through $$(3, 1)$$, giving your answer in slope-intercept form.

$$y = -4x + 13$$

Problem Statement

Determine the equation of the line that is perpendicular to $$x - 4y = 15$$ and passes through $$(3, 1)$$, giving your answer in slope-intercept form.

Solution

### 2730 video solution

$$y = -4x + 13$$

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line: $$y = -3x + 2$$ point: $$(3, 5)$$

Problem Statement

Write the equation of the line that contains the point $$(3, 5)$$ and is perpendicular to the line $$y = -3x + 2$$, giving your answer in slope-intercept form.

$$y = x/3 + 4$$

Problem Statement

Write the equation of the line that contains the point $$(3, 5)$$ and is perpendicular to the line $$y = -3x + 2$$, giving your answer in slope-intercept form.

Solution

### 2731 video solution

$$y = x/3 + 4$$

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line: $$y = 2x + 1$$ point: $$(-4, 5)$$

Problem Statement

Determine the equation of the line that is perpendicular to $$y = 2x + 1$$ and passes through $$(-4, 5)$$, giving your answer in slope-intercept form.

$$y = -x/2 + 3$$

Problem Statement

Determine the equation of the line that is perpendicular to $$y = 2x + 1$$ and passes through $$(-4, 5)$$, giving your answer in slope-intercept form.

Solution

### 2732 video solution

$$y = -x/2 + 3$$

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line: $$y = 5x - 3$$ point: $$(2, -1)$$

Problem Statement

Find the equation of the line perpendicular to the line $$y = 5x - 3$$ that passes through the point $$(2, -1)$$, giving your answer in slope-intercept form.

$$y = -x/5 - 3/5$$

Problem Statement

Find the equation of the line perpendicular to the line $$y = 5x - 3$$ that passes through the point $$(2, -1)$$, giving your answer in slope-intercept form.

Solution

### 2733 video solution

$$y = -x/5 - 3/5$$

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line: $$y = 3x/4 - 1$$ point: $$(8, -3)$$

Problem Statement

Find the equation of the line perpendicular to the line $$y = 3x/4 - 1$$ that passes through the point $$(8, -3)$$, giving your answer in slope-intercept form.

$$y = -4x/3 + 23/3$$

Problem Statement

Find the equation of the line perpendicular to the line $$y = 3x/4 - 1$$ that passes through the point $$(8, -3)$$, giving your answer in slope-intercept form.

Solution

### 2734 video solution

$$y = -4x/3 + 23/3$$

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line: $$y = -2x/3 + 4$$ point: $$(6, -2)$$

Problem Statement

Find the equation of the line perpendicular to the line $$y = -2x/3 + 4$$ that passes through the point $$(6, -2)$$, giving your answer in slope-intercept form.

$$y = 3x/2 - 11$$

Problem Statement

Find the equation of the line perpendicular to the line $$y = -2x/3 + 4$$ that passes through the point $$(6, -2)$$, giving your answer in slope-intercept form.

Solution

### 2735 video solution

$$y = 3x/2 - 11$$

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line: $$y=2x+1$$ point: $$(2,0)$$.

Problem Statement

Find the equation of the line, in slope-intercept form, perpendicular to $$y=2x+1$$ through the point $$(2,0)$$.

$$y = -x/2 + 1$$

Problem Statement

Find the equation of the line, in slope-intercept form, perpendicular to $$y=2x+1$$ through the point $$(2,0)$$.

Solution

### 2736 video solution

$$y = -x/2 + 1$$

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line: $$y=-9x+5$$ point: $$(3,9)$$

Problem Statement

Find the equation of the line, in slope-intercept form, perpendicular to $$y=-9x+5$$ through the point $$(3,9)$$.

$$y = x/9 + 26/3$$

Problem Statement

Find the equation of the line, in slope-intercept form, perpendicular to $$y=-9x+5$$ through the point $$(3,9)$$.

Solution

### 2737 video solution

$$y = x/9 + 26/3$$

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