What is the equation of the line that passes through points #(1,4)# and #(3,2)#?

How do you write it in slope-intercept and general form?

1 Answer
May 30, 2016

#f(x)=-x+5#

Explanation:

Since the question speaks of a line, we assume that this is a linear function that follow the generic equation #f(x)=ax+b#, where #f(x)=y# and #a# and #b# are coefficients . We may begin by extraction the values for #x# and #y# from the points given and make a system of equations:

#{4=a+b#
#{2=3a+b#

This system can be solved by two ways. I'm going show it using the substitution method, but the additive method works as well. Therefore, isolate either #a# or #b# in the first equation:

#{4=a+b => b=4-a#
#{2=3a+b#

Then substitute it in the other equation:

#2=3a+(4-a)#
#2=2a+4#
#2a=-2#
#a=-1#

Since # b=4-a#, then #b=4-(-1)=5#

Notice that the negative sign of #a# was expected, since the function is downwards inclined. For making the final answer, lets substitute the coeficients #a# and #b# in the gerenal equaion:

#f(x)=-x+5#