Question

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

Answer 1

Answer:

The equation of the line is:

$y = -\frac{1}{3}x - 2$

Step-by-step 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: $m = \frac{2}{-6} = -\frac{1}{3}$

So the equation of the line is:

$y = -\frac{1}{3}x - 2$