What is the equation of the line between #(6,5)# and #(2,9)#?

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Answer 1 · 2018-03-03T16:39:27

#y=-x+11#

The gradient of the line is found using the equation

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

Substituting #y_1 = 5, y_2 =9 and x_1 = 6, x_2 = 2# we get:

m = #(9-5)/(2-4) = 4/-4 = -1#

Using the formula for a line #y = mx+c# and knowing that # m= -1# and having a point we can work out the equation of the line:

#5 = -1(6)+c#
#5 = -6+c#
#11=c#

Therefore:

#y = -x+11#