What is the equation of the line passing through #(5,12)# and #(14,2)#?

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Answer 1 · 2015-11-18T13:51:42

#y=-1/9(10x-158)#

Assumption: Strait line passing through given points!
The left most point #->(5,12)#

Standard form equation: #y=mx+c" ............(1)"#
Where m is the gradient.

Let
#(x_1,y_1)-> (5,12)#
#(x_2,y_2)->(14,2)#

Then #color(green)(m =("Change in y-axis")/("Change in x-axis") = (y_2-y_1)/(x_2-x_1)=(2-12)/(14-5) =(-10)/(9))#

As the gradient (m) is negative then the line 'slopes' downward from left to right.

Substitute value of #(x_1,y_1)# for the variables in equation (1) giving:

#12= (-10/9 times 5)+c#

#c= 12+(10/9 times 5)#

#color(green)(c= 12 +50/9 -= 158/9)#

So #y=mx+c -> color(blue)(y= (-10/9)x + 158/9)#

#color(blue)(y=-1/9(10x-158))#