Question 55501
You know right away that this is a line. Every $0.25 change in price means a change of 40 customers...a linear relationship. Besides, they ask for the slope...that's a characteristic of a line.
Let's find the slope. At $2.25, 800 customers ride the bus. At $2.50, 760 folks will ride the bus. Remember the formula for slope m=(y2-y1)/(x2-x1)
Here's what I get when I plug it in:
m = (760-800)/(2.5-2.25)
m = -40/.25
m = -160
The slope of the line is -160 passengers per dollar.
Let's come up with an equation for our bus-rider line. In slope-intercept form, its y=mx+b
We know m, and we can plug in a point for x and y. Lets do that:
800 = -160(2.25)+b
Simplifying
800 = -360 +b
And adding 360 to both sides
1160 = b
Our line is y = -160x+1160
If we make the bus free (ie.. set x=0), how many people will ride? Let's see
y=-160(0)+1160
y = 1160
1160 folks will ride the bus max.
Ok...what price will cause there to be no riders (ie...set y=0)?
0 = -160x +1160
-1160 = -160x
7.25 = x
7.25 is the price that will cause nobody to ride the bus