What is the equation in point-slope form of the line given (4, –4) and (9, –1)?

1 Answer
May 17, 2015

Firstly in this question we would need to find the "slope" or otherwise known as the gradient. we use the formula.

#m= (Y2 - Y1)/(X2-X1)#

so for this question we get.

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

#m = 3/5#

now we take a look at our equation for a straight line, which is.

#Y = mX + c#

we have now got a value for #m# and we need to solve for a value for #c#.

to do this, we use the #X# and #Y# from either of the given points and put them into our formula. so we have:

#-4 = (3/5)(4) + c#
# -4 = (12/5) + c#
#-4 - (12/5) =c#

#c = -32/5#

now all we need to do is insert our value for #c# into our straight line equation. thus we end up with.

#Y = (3/5)X - (32/5)#