# How do you write an equation of the line that passes through (–3, –5) and (3, 0)?

##### 2 Answers

The equation of the line is:

#### Explanation:

The equation of the line will be in the form:

where

To find the slope, we use:

It doesn't matter which point we decide is

Now we can use the slope and the coordinates of one point - either will do - to find the y-intercept:

Rearranging:

Over all, then, the equation of the line is:

The line is

#### Explanation:

The general equation of a line is given by

$$y=mx+q$$

so we need to substitute our two points and solve the two equations that we will obtain.

First equation: the point is

$$-5=-3m+q.$$

Second equation: the point is

$$0=3m+q.$$

From the second equation we have

$$q=-3m$$

that we can substitute in the first equation obtaining

$$-5=-3m-3m$$

$$-5=-6m$$

$$5=6m$$

$$m=5/6$$

and, consequently

$$q=-3m=-3\times5/6=-5/2.$$

So the equation of the line is

$$y=5/6x-5/2.$$

To be sure that the line is correct we can substitute the two points and see that we obtain the identities. First point

$$-5=-3\times5/6-5/2$$

$$-5=-5/2-5/2$$

$$-5=-5.$$

Second point

$$0=3\times 5/6-5/2$$

$$0=5/2-5/2$$

$$0=0.$$