MHB Finding the Linear Equation Relating Price and Number of Widgets Sold

[woof123]

Okay here's the question:

If you sell widgets for 2 dollars, you sell 300 per day. If you sell them for 4 dollars, you sell 200 per day. assume linear relat., between price (x) and # widgets sold per day (y), write linear equation relating x and y

I'm thinking I plot the x,y pairs, then calculate slope and the y intercept in order to put it into y=mx+b form...does that make sense?

 

[MarkFL]

You have two points on the graph, so you can compute the slope as follows:

$$m=\frac{\Delta y}{\Delta x}=\frac{y_2-y_1}{x_2-x_1}$$

Then, you can use either point (I'll use the first), and the slope you computed, in the point-slope formula:

$$y=m(x-x_1)+y_1$$ :D

 

[HallsofIvy]

Equivalently, any linear function can be written y= ax+ b for numbers a and b. The fact that y(2)= 300 means that 2a+ b= 300. The fact that y(4)= 200 means that 4a+ b= 200. Solve those two equations for a and b.

(An obvious point is that there is "b" with coefficient 1 in both equations. Subtracting one equation from the other eliminates b leaving a single equation for a. Do you see that this is the same as your formula for slope? And then using that value of a in one of the two equations to find b is the same as MarkFL suggests.)