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91Ó°ÊÓ

In the following exercises, find an equation of a line parallel to the given line and contains the given point. Write the equation in slope–intercept form.

line x = 4, point (−2, −1)

Short Answer

Expert verified

Equation of parallel line to x = 4 passing through the point (-2, -1) is x = -2.

Step by step solution

01

Step 1.  Given information

Equation of the line is, x = 4

Given point is (-2, -1)

02

Step 2. Concept

First need to write original equation in the form of y = mx + b.

Then we will use slope - point formula to find the equation of parallel line to the original line passing through the given point.

03

Step 3. Explanation

We have given equation is the x = 4 which is the vertical line passing through the point (4, 0) and we know that the slope of the vertical lines is ∞.

If the slope of a line is undefined, then the line is a vertical line, so it cannot be written in slope - intercept form, but it can be written in the form: x=a, where a is a constant.

That is the line passing through the point (-2, -1) is vertical line x = -2.

04

Step 4. Conclusion

Hence, equation of parallel line to x = 4 and passing through the point (-2, -1) is y = -2.

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