Finding The Equation Of A Line, Given The Slope And A Point

This video explains how to find the equation of a line, given a point and the slope of the line.

There are two ways of solving this.

One way is using the slope-intercept formula, y = mx + b

And the other way is by using the point-slope formula, $y - y_1 = m(x - x_1)$

Video-Lesson Transcript

Let’s go over finding the equation of a line, given a point and the slope.

We’re going to use the slope intercept formula:

$y = mx + b$

For example:

$(2, 5)$, $m = -2$

We’re going to solve this in two different ways.

First is the point-slope formula which is

$y - y_1 = m (x - x_1)$

Now, let’s substitute

$y - 5 = -2 (x - 2)$

Now, let’s manipulate this to get the slope intercept form

$y - 5 = -2x + 4$

Now, let’s isolate $y$ by adding $5$ on both sides.

$y - 5 + 5 = -2x + 4 + 5$
$y = -2x + 9$

Or the second way to solve this is to do the slope intercept form directly.

$y = mx + b$
$y = -2x + b$

Let’s solve for $b$ by substituting the values of $x$ and $y$.

$5 = -2(2) + b$
$5 = -4 + b$

Then isolate $b$ by adding $4$ on both sides

$5 + 4 = -4 + 4 + b$
$9 = b$

Now let’s write our slope intercept form

$y = -2x + 9$

which is the same as our first answer.