Point-Slope Form 03:36 minutes

Video Transcript

Transcript Point-Slope Form

A trio of busy business beavers gets together to make plans for the current year’s production of logs. Last year was problematic and they don't want to make the same mistake this year.

Last year, the beavers took a long vacation in the middle of the year and they had to work a lot of overtime just to reach their yearly goal. A member of the group has something to say about the plan, but the boss beaver won't let him speak.

The big boss goes on and on and on... The boss wants to plan for steady production throughout all twelve months. To figure this out, the beavers need some help calculating the equation of a line. Let's help them.

Point-slope Form and Slope Formula

The beavers, and you, can use two equations to figure out a steady production plan: the point-slope form & slope formula. I'll write the formulas down.

M stands for the slope of a line. Why M? No one knows for sure. What we do know is ordered pairs (x1, y1) and (x2, y2) are known points on the line, and the ordered pair (x, y) is any unknown point on the line.

Note how these two formulas are really just the same formula presented in two different ways. Why do we need to use two versions of the same formula? Well, stay tuned and you’ll see why two is better than one.

Point-slope Form Calculation 1

At the beginning of the year, the busy beavers have 20 logs in storage. To make sure they have enough logs for the annual winter festival, they need to have 180 logs in storage by the end of the tenth month.

Based on this steady production schedule, for each month, how many logs do the beavers need to produce and store?

To solve this problem, since we do know two points on the line, but we don't know the slope. The formula to determine the slope of the line is the best choice.

M is equal to difference of the two y-coordinates divided by the difference of the two x coordinates. Let's plug in the numbers.

The slope is equal to 180 minus 20 over 10 minus zero, that’s 160 over ten, which is equal to 16. To meet their production goal, they must produce 16 logs each and every month.

Point-slope Form Calculation 2

And, if they stay on this same production schedule, how many logs will they have in storage at the end of the twelve months?

Since we know the slope is equal to 16, and we know at least one point on the line, the point-slope form is easier to use to calculate the number of logs that will be produced and stored at the end of 12 months - if the beavers can stay on schedule, that is.

  • Plug the numbers into the formula, y minus y1 is equal to the slope times the difference of x and x1.
  • When we evaluate this, we get: Y is equal to two hundred twelve.

Awesome, problem solved! Check out the graph!

Now the beavers can get to work, to stay on schedule, they must produce 16 logs every month. That same member of the committee is still trying to speak, but the big boss only wants to listen to himself talk. I wonder what he wants to say.

Oh no! There’re no more trees! That must be what he was trying to say all along. I guess it's back to the drawing board...