Question 417963
"Write the equation of the line passing through the points (-2, 7) and (3,-5)"


One way to get the equation of a line,
is to find the slope and y-intercept.
Then, substitute those into the slope-intercept form: y = mx + b



(-2,7) , (3,-5)

y2 - y1
-------- {formula to find slope}
x2 - x1


-5 - 7
-------- {substituted into slope formula}
3 - (-2)


-12
--- {simplified}
5 


slope is -12/5


Now, pick one of the points, and substitute it with the slope, into slope-intercept form.  
This will give you the y-intercept.


(3,-5), m = -12/5
y = mx + b {slope-intercept form}
-5 = -12/5(3) + b {substituted into slope-intercept form}
-5 = -36/5 + b {multiplied -12/5 by 3}
b = 11/5 {added 36/5 to both sides}
y-intercept is 11/5


Substitute slope and y-intercept into slope-intercept form y = mx + b
m is the slope 
b is the y-intercept


y = -12/5x + 11/5
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