Question

What is the equation of the line passing through `(93,78)` and `(-68,44)`?

Answer 1

Find the line in the form `y = mx + b`.
The slope can be found through the formula `m=(y_2-y_1)/(x_2-x_1)`.
Thus, `color(red)(m)=(44-78)/(-68-93)=(-34)/-161=color(red)(34/161)`

Now, find `b` by plugging `m` into `y = mx + b` with one of the points.

With the point `(93,78)`: `78 = (34/161)93+b`
Multiply: `78 = 3162/161+b`
Find a common denominator: `12558/161=3162/161+b`
Subtract `3162/161` from both sides: `color(red)(9396/161=b)`
This cannot be simplified.

Plug back into `y=mx+b`: `color(red)(y=34/(161)x+9396/161)`

This can also be written as `y=(34x+9396)/161`