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