Hemoglobin A1c reading of 6.5 corresponds to an average blood glucose level of 135. hemoglobin A1c reading of 6.0 corresponds to an average blood glucose level of 120. Let y represent the average blood gulcose level and x represent the hemoglobin A1c?

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Answer 1 · 2018-04-18T12:29:43

#color(blue)(y=30x-60)#

So we have these points:

#(6.5,135)# and #(6,120)#

The gradient(slope) is given as:

#(y_2-y_1)/(x_2-x_1)#

Using

#y_2=120#

#y_1=135#

#x_2=6#

#x_1=6.5#

#:.#

#(120-135)/(6-6.5)=(-15)/(-0.5)=30#

So the slope is 30:

We can find the equation using the slope point form of a line:

#(y_2-y_1)=m(x_2-x_1)#

Where #m# is the slope.

Using one of the coordinates, say #(6,120)# and the slpope we just found. Plug these in:

#(y-120)=30(x-6)#

#y-120=30x-180#

#y=30x-180+120#

#y=30x-60#

The graph shows this to be correct:

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