cassie was able to sell 110 shirts when the price is 75 pesos and 200 shirts when she lowered it to 60 pesos. What's the y-intercept in the problem?

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mvcdc | Student, Graduate | (Level 2) Associate Educator

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First, let us identify the variables. The independent variable (for x) is the price, while the dependent variable (for y) is the number of shirts used. 

Hence, we have the following: `x_1 = 75, y_1 = 110, x_2 = 60, y_2 = 200` .

We first get the line that passes through the two points using the two-point form of the equation of the line:

`y - y_1 = (y_2 - y_1)/(x_2 - x_1) (x - x_1)`

`y - 110 = (200 - 110)/(60 - 75) (x - 75)`

`y - 110 = (90/-15) (x - 75)`

`y - 110 = -6 (x - 75)`

`y - 110 = -6x + 450`

`y = -6x + 450 + 110`

`y = -6x + 560`

This equation represents the line that passes through the two points. We then get the y-intercept of this line by setting `x=0` .` `

Hence, the y-intercept is y = -6*0 + 560 = 560.

(Note: One should be cautious in interpreting the result. The point (0, 560) is the y-intercept of the line passing through the two given points. However, recall that x is the price and y is the number of shirts sold. This means that when the shirts are free (0 price), 560 items will be "sold". This might not actually be true in real life (as we mightexpecteveryone to avail of the free stuff), but we can definitely see the law of demand and law of supply -- as the price drops the demand increases.)

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