Answer:
- a = 600 -100p
- a = 450 for p = 1.50
Step-by-step explanation:
You want the formula that represents (p, a) = (3.50, 250) and (2.50, 350) as a linear function. Then you want the value of 'a' for p = 1.50.
Slope
We can see from the ordered pairs that 'a' goes up by 100 when p goes down by 1.00. The slope is ...
m = ∆a/∆p = 100/(-1) = -100
Intercept
The y-intercept (b) can be found by solving the slope-intercept equation for b:
y = mx +b
b = y - mx
For (x, y) = (3.50, 250), the value of 'b' is ...
b = 250 -(-100)(3.50) = 600
Equation
The slope-intercept equation for 'a' in terms of p is ...
a = -100p +600
Evaluation
The value of 'a' for p = 1.50 is ...
a = -100(1.50) +600
a = 450
They will sell 450 items if the price per item is $1.50.
