How do you find the equation of the line passing through the points (4, 2) and (3, -4)?

1 Answer
smendyka
Dec 13, 2016

#y - 4 = 6(x - 2)# or #y = 6x - 8#

Explanation:

First, we need to find the slope of the equation. The formula for the slope of a linear equation is:

#color (red)(m = (y_2 - y_1)/(x_2 - x_1))# where #color(red)(m)# is the slope and the two points are: #color(red)(((x_1, y_1)))# and #color(red)(((x_2, y_2)))#

Substituting our points gives the slope as:

#m = (-4 - 2)/(3 - 4)#

#m = (-6)/(-1)#

#m = 6#

We can now use the point-slope formula to find the equation of the 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 given point on the line.

Substituting the information we have gives:

#y - 4 = 6(x - 2)#

or, converting to standard form:

#y - 4 = 6x - 12#

#y - 4 + 4 = 6x - 12 + 4#

#y - 0 = 6x - 8#

#y = 6x - 8#

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