What is the equation of the line passing through #(11,13)# and #(59,67)#?

1 Answer
Nov 18, 2015

#y=1.125x + 0.625#
or
#y=9/8 x + 5/8#

Explanation:

First label the coordinates.
#x1 = 11, y1 =13#
#x2 = 59, y2 = 67#

The slope (m) is the rise (change in y) divided by the run (change in x),
so #m = (y2 - y1)/(x2-x1)#

#m = (67-13)/(59-11) = 54/48 = 9/8 = 1.125#

The standard linear formula is #y=mx+b# and we have to find b. Substitute m and one set of coordinates into this formula:

#y1=m*x1+b-> 13 = 1.125 * 11 + b -> 13 = 12.375 +b#

#b=0.625#

Substitute this into #y=mx+b -> **y = 1.125 x + 0.625** #

Always check your answer by substituting the other set of coordinates into the equation:

#y = 1.125 * **59** +0.625 = 66.375 + 0.625 = 67#

Since this matches the original coordinate (59, 67), the answer must be correct.