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

Mar 12, 2018

In slope intercept form, the answer should be: $y = 1.8136 x + 18.2034$ or in fractional terms, $y = \frac{107}{59} x + \frac{1074}{59}$

#### 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

$m = \frac{{y}_{2} - {y}_{1}}{{x}_{2} - {x}_{1}}$

plugging in the two sets of coordinates:

$m = \frac{98 - \left(- 9\right)}{44 - \left(- 15\right)} \Rightarrow \textcolor{red}{m = \frac{107}{59} = 1.8136}$

And now we have our slope.

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

$y = m x + b$

$- 9 = \frac{107}{59} \cdot \left(- 15\right) + b \Rightarrow - 9 = - \frac{1605}{59} + b$

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

$- 9 - \left(- \frac{1605}{59}\right) = b$

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

$b = \frac{1605 - 531}{59} \Rightarrow \textcolor{red}{b = \frac{1074}{59} = 18.2034}$

now we can fill out the slope intercept equation:

$y = \frac{107}{59} x + \frac{1074}{59}$

$y = 1.8136 x + 18.2034$