How do you write an equation given points (5,7), (6,8)?

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Answer 1 · 2016-11-13T20:50:17

#y=x+2#

First, find the slope of the line using slope formula:

#m=(y_2-y_1)/(x_2-x_1)#

Where #m# is the slope

#(5,7)=>(x_1,y_1)#

#(6,8) => (x_2,y_2)#

#m=(8-7)/(6-5)=1/1=1#

Next, pick a set of coordinate points and plug them into point slope form:

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

And the slope of #1#

If you use #(5,7)#:

#y-7=1(x-5)#

Distribute the one throughout the set of parenthesis

#y-7=x-5#

Add #7# on both sides of the equation

#y=x+2#

If you were to use the other set of coordinate points, the equation should be the same:

If you use #(6,8)#:

#y-8=1(x-6)#

Distribute the one throughout the set of parenthesis

#y-8=x-6#

Add #8# on both sides of the equation

#y=x+2#