Question

A line contains the points (6,-4) and (0,-2). What is the equation of the line?

Answer 1

The equation of the line is:

`y = -(1)/(3)x - 2`

Explanation:

Equation of a line:

The equation of a line has the following format:

`y = mx + b`

In which m is the slope and b is the y-intercept, that is, the value of y when x = 0.

(0,-2)

This means that the y-intercept is -2, that is,
`b = -2`. So

`y = mx - 2`

Finding the slope:

When we have two points, the slope is given by the change in y divided by the change in x.

We have points (6,-4) and (0,-2).

Change in y: -2 - (-4) = -2 + 4 = 2

Change in x: 0 - 6 = -6

Slope:
`m = (2)/(-6) = -(1)/(3)`

So the equation of the line is:

`y = -(1)/(3)x - 2`