How do you write an equation of a line that passes through the point (3, 2) and is parallel to the line y=3x-4?

1 Answer
smendyka
Dec 16, 2016

#y - 2= 3(x - 3)# or #y = 3x - 7#

Explanation:

For a line to be parallel to another line, by definition it must have the same slope. Because the equation is in the slope-intercept form we can use the slope of the line.

The slope-intercept form of a linear equation is:

#color(red)(y = mx + b)#
Where #m# is the slope and #b# is the y-intercept value.

Therefore, for the given equation the slope is #3#.

Now we can use the point slope formula to determine the equation for the parallel line.

The point-slope formula states: #color(red)((y - y_1) = m(x - x_1))#
Where #m# is the slope and #(x_1, y_1) is a point the line passes through.

Substituting the slope from the given line and the given point gives:

#y - 2= 3(x - 3)#

Transforming this to the slope-intercept form by solving for #y# gives:

#y - 2 = 3x - 9#

#y - 2 + 2 = 3x - 9 + 2#

#y = 3x - 7#

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