## 17Calculus Precalculus - Parallel Lines

##### 17Calculus

Parallel Lines

When two lines are parallel, their slopes are equal. So, for two lines in slope intercept form $$y = mx + b_1$$ and $$y=mx + b_2$$, the slopes $$m$$ are the same but $$b_1 \neq b_2$$ (unless of course they are the same line). One of the nice things about the slope intercept form, $$y = mx + b$$ is that you can pull the slope $$m$$ and the y-intercept $$b$$ directly from the equation without having to do any work. For the two parallel lines, the slopes are the same but they cross the y-axis at different points.

Okay, let's watch a great video on parallel and perpendicular lines.

### Finding Equations of Parallel and Perpendicular Lines

Okay, time for some practice problems.

Practice

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

line: $$3x-y/4 = 2$$ point: $$(1/6,-8)$$

Problem Statement

Find the equation of the line, in slope-intercept form, parallel to $$3x-y/4 = 2$$ going through the point $$(1/6,-8)$$.

$$y=12x-10$$

Problem Statement

Find the equation of the line, in slope-intercept form, parallel to $$3x-y/4 = 2$$ going through the point $$(1/6,-8)$$.

Solution

### 2720 video solution

$$y=12x-10$$

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

Problem Statement

Write the equation of the line that is parallel to $$x - 2y = 6$$ and passes through the point $$(-4, 3)$$, giving your answer in slope-intercept form.

$$y = x/2 + 5$$

Problem Statement

Write the equation of the line that is parallel to $$x - 2y = 6$$ and passes through the point $$(-4, 3)$$, giving your answer in slope-intercept form.

Solution

### 2721 video solution

$$y = x/2 + 5$$

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

Problem Statement

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

$$y = -5x - 1$$

Problem Statement

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

Solution

### 2722 video solution

$$y = -5x - 1$$

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line: $$3x+2y = 12$$ point: $$(2, -5)$$

Problem Statement

Determine the equation of the line that is parallel to $$3x+2y = 12$$ and passes through $$(2, -5)$$, giving your answer in slope-intercept form.

$$y = -3x/2 + 6$$

Problem Statement

Determine the equation of the line that is parallel to $$3x+2y = 12$$ and passes through $$(2, -5)$$, giving your answer in slope-intercept form.

Solution

### 2723 video solution

$$y = -3x/2 + 6$$

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

Problem Statement

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

$$y = 2x + 3$$

Problem Statement

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

Solution

### 2724 video solution

$$y = 2x + 3$$

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

Problem Statement

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

$$y = 3x - 14$$

Problem Statement

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

Solution

### 2725 video solution

$$y = 3x - 14$$

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

Problem Statement

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

$$y = 3x/2 - 9$$

Problem Statement

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

Solution

### 2726 video solution

$$y = 3x/2 - 9$$

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line: $$x+7y=4$$ point: $$(7,9)$$

Problem Statement

Find the equation of the line, in slope-intercept form, parallel to $$x+7y=4$$ through the point $$(7,9)$$.

$$y=-x/7+10$$

Problem Statement

Find the equation of the line, in slope-intercept form, parallel to $$x+7y=4$$ through the point $$(7,9)$$.

Solution

### 2727 video solution

$$y=-x/7+10$$

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