What is the equation of the line passing through #(8,2), (5,8)#?

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Answer 1 · 2016-01-04T17:26:35

In general form:

#2x+y-18 = 0#

The slope #m# of a line passing through two points #(x_1, y_1)# and #(x_2, y_2)# is given by the equation:

#m = (Delta y)/(Delta x) = (y_2-y_1)/(x_2-x_1)#

Let #(x_1, y_1) = (8, 2)# and #(x_2, y_2) = (5, 8)#

Then:

#m = (8-2)/(5-8) = 6/(-3) = -2#

The equation of the line passing through #(8, 2)# and #(5, 8)# can be written in point slope form as:

#y - y_1 = m(x-x_1)#

That is:

#y - 2 = -2(x - 8)#

Add #2# to both sides to find:

#y = -2x+18#

which is the slope intercept form of the equation of the line.

Then putting all terms on one side by adding #2x-18# to both sides we find:

#2x+y-18 = 0#

which is the general form of the equation of a line.