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

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

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