Equations of Parallel Lines

Algebra 1 Tutorial

Equations of Parallel Lines

Intro

Non-vertical lines, or lines that have positive, negative or undefined slope, are parallel if they have the same slope and different y-intercepts. Vertical lines, which have zero slope, are parallel if they have the same slope and different x-intercepts.

Sample Problem

Write the equation of the line that passes through (4,-4) and is parallel to
y=3x-2.

Solution

To find an equation of a line that is parallel to a given line and goes through a particular point, we start by making sure the equation of the given line is written in point-slope form, which is y – y1 = m(x – x1).

The slope of y=3x-2 is 3, and we are looking for a line that passes through (4,-4). We substitute the coordinates of the point into the point-slope equation as x1 and y1, so our new equation in point-slope form will be:
y-(-4) = 3(x-4)

First, let’s rewrite the equation by changing the sign of “-(-4)” to a positive, because a negative number times a negative number is positive.
y+4 = 3(x-4)

Next, we use the distributive property and then solve for y.
y+4 = 3x+3(-4)
y+4 = 3x-12
y+4-4 = 3x-12-4
y = 3x-16

The equation of the line that passes through (4,-4) and is parallel to y=3x-2 is y=3x-16.



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