What is the equation of the line passing through #(44,98)# and #(-15,-9)#?

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Answer 1 · 2018-03-12T19:01:36

In slope intercept form, the answer should be: #y=1.8136x+18.2034# or in fractional terms, #y=107/59x+1074/59#

The first step is to calculate the slope of the line, and the second is to calculate the intercept based on a known set of coordinates.

Step 1: Calculate the slope. Linear slope can be easily written as

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

plugging in the two sets of coordinates:

#m=(98-(-9))/(44-(-15)) rArr color(red)(m= 107/59 = 1.8136)#

And now we have our slope.

Next, we need to solve for the intercept. Let's use the #(-15, -9)# to determine the intercept.

#y=mx+b#

#-9=107/59*(-15)+b rArr -9=-1605/59+b #

Next, we'll bring our fraction to the Left-Hand Side (LHS) and solve for #b#:

#-9-(-1605/59)=b#

To make the fractional math easier, lets raise -9 to the common denominator of 59:

#-531/59-(-1605/59)=b rArr -531/59+1605/59)=b#

#b=(1605-531)/59 rArr color(red)(b=1074/59=18.2034)#

now we can fill out the slope intercept equation:

#y=107/59x+1074/59#

#y=1.8136x+18.2034#