In a linear relationship two data points are #(9,3)# and #(33,9)#. If the function is #y=mx+b#, we have?

Question

(a) #m=4# and #b=-33#
(b) #m=1/4# and #b=3/4#
(c) #m=4# and #b=-123#
(d) #m=1/4# and #b=24#

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Answer 1 · 2017-01-08T11:50:26

Looking at my calculations and your question's structure you have asked for the wrong thing. You need the value of #m# and not #b#

#m=1/4 -> "multiple choice a"#

Let point 1 #->P_1->(x_1,y_1)=(9,3)#
Let point 2 #->P_2->(x_2,y_2)=(33,9)#

gradient #->m=("change in y")/("change in x") # as you read left to right on the graph.

#=>m=(y_2-y_1)/(x_2-x_1)=(9-3)/(33-9) = 6/24 -=(6-:3)/(24-:3) = 2/8 = 1/4#

Answer 2 · 2017-01-08T15:30:48

Answer is (b)

As the two data points given in #(x,f(x))# form are #(9,3)# and #(33,9)#

the linear relation is #(y-y_1)/(y_2-y_1)=(x-x_1)/(x_2-x_1)#, where #y=f(x)#

i.e. #(y-3)/(9-3)=(x-9)/(33-9)#

or #(y-3)/6=(x-9)/24#

or #y-3=(x-9)/4#

or #4y-12=x-9#

or #4y=x-9+12=x+3#

or #y=x/4+3/4#

i.e. #f(x)=1/4xx x+3/4#

Hence, while #m=1/4#, #b=3/4#

and answer is (b)