Question

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

Answer 1

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

Explanation:

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`