Question 86855
Question:



find the slope intercept form (y=mx+b) of the equation for the line that satisfy the following:
passes through the points (3,-1) and (1,4)



Answer:

You want to find the equation for a line that passes through the two points:

(3,-1) and (14,).

First of all, remember what the equation of a line is:

y = mx+b,  Where:     m is the slope, and     b is the y-intercept



First, let's find what m is, the slope of the line...



slope is given by the formula, {{{ m = (y2 - y1)/ (x2 - x1)}}}


==> {{{ m = (4 - (-1))/ (1 - 3)}}}



==> {{{ m = (5)/ (-2)}}}



==> {{{ m = 5/ (-2)}}}



Now equation of a line is given by,    y = mx + b



Now plug any of the given point in this equation.


Lets take the first point ( 3, -1)


==> {{{ -1 = (5/2)* (-3) + b}}}





==> {{{ -1 = (-15/2) + b}}}




==> {{{ -1 +(15/2) =  b}}}




==> {{{ 13/2  =  b}}}



That is {{{ b = 13/2}}}



[If you take the second point also you will get the same value for b]




So the equation of the line :


{{{ y = (-5/2)*x  + (13/2)}}}


Which is the required equation of the line.



Hope you found the explanation useful


Warm regards.


Praseena.