Question

What is the equation of the line passing through `(3,-5)` and `(42,1)`?

Answer 1

Both points satisfy the line equation `y=mx+b`, so you need to find `m` and `b`

Explanation:

Since both points satisfy the equation, we know that:

`-5=m*3+b`, and

`1=m*42+b`

We now have a system of two equations with `m` and `b`. To solve it we can subtract the first from the second equation to eliminate `b`:

`6=39m` and so `m=6/39=2/13`. From the first equation now we have:

`-5-(2/13)*3=b`, and so `b=-65/13-6/13=-71/13`.

The equation of the line is then:

`y=2/13x-71/13`