A farmer finds there is a linear relationship between the...

Name: A farmer finds there is a linear relationship between the number of bean stalks, n, she plants and the yield, y, each plant produces. When she plants 30 stalks, each plant yields 30 oz of beans. When she plants 33 stalks, each plant produces 29 oz of beans. Find a linear relationship in the form y = mn + b that gives the yield when n stalks are planted.
Uploaded: 2022-06-06T13:30:05-08:00
Duration: 3 min 50 s
Channel: Tim Guindon
Description: A farmer finds there is a linear relationship between the number of bean stalks, n, she plants and the yield, y, each plant produces. When she plants 30 stalks, each plant yields 30 oz of beans. When she plants 33 stalks, each plant produces 29 oz of beans. Find a linear relationship in the form y = mn + b that gives the yield when n stalks are planted.

A farmer finds there is a linear relationship between the number of bean stalks, n, she plants and the yield, y, each plant produces. When she plants 30 stalks, each plant yields 30 oz of beans. When she plants 33 stalks, each plant produces 29 oz of beans. Find a linear relationship in the form y = mn + b that gives the yield when n stalks are planted.

Transcript

00:01 All right, so we are told that we have a linear relationship.

00:04 So we're going to use the equation of a line.

00:06 Y equals m.

00:07 We're going to use this mn plus b.

00:10 So we're trying to find the equation of a line.

00:13 And we're given some data points.

00:15 We're given some information here.

00:16 We're given.

00:19 So for stocks being the letter n, producing a yield, which represented by the letter y, when she plants 30 stocks, it yields 30 ounces.

00:31 Of beans.

00:32 Once you plants 33 stocks, it produces 29 ounces.

00:38 So we want to see this as kind of two different data points, two different coordinate points.

00:43 We can see it's like a 30 comma 30 and a 33 comma 29.

00:46 So to find the equation of a line, we are looking for two values, m and b.

00:53 Now in a linear discussion, m is your slope or your rate of change, how the yield changes per stalk that you add, and b, in a visual sense, we're thinking that's our y intercept.

01:08 So to get this equation, we need to figure out what m and b are given just these two points.

01:15 So let's start with m.

01:17 So again, m is my slope.

01:21 And we typically use the slope equation of rise over run or change in y over change in x or y2 minus y1 over x2 minus x1.

01:32 Now, no, we don't have x's in y's.

01:34 We have ends in y's.

01:36 But the stocks, these are the independent variable here.

01:40 So those are representing my x values.

01:44 So as i look at this, i'm looking at the difference of my y's.

01:47 So i'm taking y minus y, so 29 minus 30 over the difference of the x is, in this case, the ends, 33 minus 30...