ShmoopTube

00:04

Linear Equations in Point Slope Form, a la Shmoop.

00:08

Garry the Gopher loves West Hills Golf Course. [Gopher appearing from a golf hole]

00:11

Almost as much as the greenskeeper loves dynamite.

00:13

Here’s Garry’s map.

00:15

He's at point (-2, 2) and the door to freedom is at (2, -4).[Garry the Gopher on a map at point -2, 2)

00:22

Garry needs to solve the equation of the line so he can find his way to freedom or else

00:26

risk getting blown to bits by the greenskeeper…[Dynamite explodes near Gopher on the golf course]

00:29

A line is in point-slope form when it looks like this:

00:33

y – y1 = m times x – x1

00:36

Here, m is the slope of the line and (x1, y1) is any fixed point on the line.

00:42

Let's use Garry's position as the fixed point (x1, y1), so x1 = -2 and y1 = 2: [Equation of point slop form on a chalkboard]

00:51

Looks like the greenskeeper also likes that point. [Greenskeeper dropping dynamite on the gophers position]

00:54

Now we need to calculate m, or slope.

00:56

We do this by finding the rise and run between the two points:

01:00

The run… the distance between the two x-points is 4…

01:03

… while the rise…the distance between the y-points… is negative six.

01:08

Slope equals rise over run, or negative 6 over 4. [equation for rise over run on a chalkboard]

01:12

This simplifies to negative three over 2.

01:15

Now we plug in the values we know. [Person plugging a lead into a port]

01:17

y1 = 2, m = -3/2, and x1= -2.

01:23

Which makes our equation y – 2 = -3/2 times x + 2 [Golf cart drives along the golf course and explodes]

01:31

He figured it out!

01:32

Looks like Garry will live to dig another day.

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