How do you write an equation of a line through: (2,4) and (5,1)?

1 Answer
smendyka
Dec 17, 2016

#y - 4 = -1(x - 2)# or #y = -x + 6#

Explanation:

To write this equation we can use the point-slope formula. To use this formula we must first determine the slope.

The slope can be found by using the formula: #color(red)(m = (y_2 = y_1)/(x_2 - x_1)#
Where #m# is the slope and #(x_1, y_1)# and #(x_2, y_2)# are the two points.

Using the two points given in the problem the slope is:

#m = (1 - 4)/(5 - 2)#

#m = -3/3#

#m = -1#

Now we can use the point-slope formula to determine the equation:

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.

Using the slope we calculate and one of the points gives:

#y - 4 = -1(x - 2)#

Solving for #y# to put this equation into the slope-intercept form gives:

#y - 4 = -x + 2#

#y - 4 + 4 = -x + 2 + 4#

#y - 0 = -x + 6#

#y = -x + 6#

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