stars584 said:
Mrs Brooks is plannng a bakesale to raise money. A survey was taken and it shows relationship between the cookies and the ost are linear and if they charge 50 cents they will sell 200 cookies and if they charge $1 cookie they will sell 50 cookies
Write an equation that shows the relationship between cost & numeber of cookies.
Should we be using variables??? If so
Let x be # of cookies
.50x= ?
x=?
I am not sure if this is right
Yes, if you are asked to write a linear relationship, you should use variables....TWO of them.
Since the number of cookies sold PROBABLY depends on the cost of a cookie, I'd
let x = cost of cookie
let y = number of cookies sold
We know that when the cost is 50 cents, they will sell 200 cookies. This is the ordered pair (50, 200)
We also know that when the cost is $1, or 100 cents, they will sell 50 cookies. This is the ordered pair (100, 50)
Ok...you have a linear relationship going through the points (50, 200) and (100, 50)
To write an equation for this relationship,
1) find the
slope of the line through (50, 200) and (100, 50):
m = (50 - 200) / (100 - 50)
m = (-150) / (50)
m = -3
Ok..
2) you know that the slope of this linear relationship is -3.
So,
y = mx + b
y = -3x + b
You know that (50, 200) is a point ON this relationship, so you can substitute 50 for x and 200 for y:
200 = -3(50) + b
200 = -150 + b
350 = b
So, the equation for the linear relationship you're looking for is
y = -3x + 350
