Question

What is the slope of the line that contains the points (2, 6) and (-1, -6)?

Answer 1

The slope of the line is 4.

Explanation:

The equation of a line has the following general format:

`y = ax + b`

In which a is the slope and b is the y-intercept(the value o y when x = 0).

Line contains the points (2, 6) and (-1, -6).

This means that when
`x = 2, y = 6`, and when
`x = -1, y = -6`.

We replace both in the general equation and solve the system of equations.

So

`x = 2, y = 6`

`6 = 2a + b`

`b = 6 - 2a`

------------

`x = -1, y = -6`

`-6 = -a + b`

We have b as a function of a in the first equation, so

`-6 = -a + 6 - 2a`

`3a = 12`

`a = (12)/(3)`

`a = 4`

The slope of the line is 4.