How do I find the equation of a linear function that passes through #(1, 7)# and #(2, 9)#?

1 Answer
AJ Speller
Sep 17, 2014

For this type of problem we have 3 distinct steps to follow.

1) Find the slope using the formula #m=((y_2-y_1))/((x_2-x_1))#

2) Find the y-intercept, #b#, by substituting in the slope , #m#, from STEP 1 and the #x# and #y# values from one of the points given in the slope intercept formula, #y=mx+b#

3) Substitute the slope, #m#, and the y-intercept, #b#, back into the slope intercept formula, #y=mx+b#.

STEP 1

#x_1=1#
#y_1=7#

#x_2=2#
#y_2=9#

#m=((y_2-y_1))/((x_2-x_1))=((9-7))/((2-1))=2/1=2#

STEP 2

#y=mx+b#

I will use the #x# and #y# values from the point #(1,7)#

#7=(2)(1)+b#
#7=2+b#
#5=b#

STEP 3

#y=mx+b#

#y=2x+5 larr SOLUTION#

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