Question

question
ryan is a salesperson who sells computers at an electronics store. he makes a base pay amount each day and then is paid a commission for every computer sale he makes. the equation ( p = 17.50x + 100 ) represents ryans total pay on a day on which he sells ( x ) computers. what is the ( y )-intercept of the equation and what is its interpretation in the context of the problem?
answer attempt 1 out of 3
the ( y )-intercept of the function is 100 which represents
the number of computers ryan sold in a day
the commission ryan makes for each computer sale
the total pay ryan makes each day
the base pay ryan makes regardless of computer sales

Explanation:

Step1: Recall y - intercept formula

The equation of a line is in the form \(y = mx + b\), where \(b\) is the y - intercept (when \(x = 0\)). In the given equation \(P=17.50x + 100\), we compare it with the slope - intercept form. Here, \(x\) is the number of computers sold, \(P\) is the total pay. When \(x = 0\) (which means the number of computers sold \(x = 0\)), we substitute \(x = 0\) into the equation: \(P=17.50(0)+100=100\).

Step2: Interpret the y - intercept in context

The variable \(x\) represents the number of computers sold. When \(x = 0\), it means Ryan has sold 0 computers. The value of \(P\) when \(x = 0\) is the pay he gets even when he makes no sales. So the y - intercept (100) represents the base pay Ryan makes regardless of computer sales. Because the base pay is the amount he gets before any commissions (commissions depend on the number of sales, \(x\)), and when \(x = 0\) (no sales), his pay is the base pay.

Answer:

The y - intercept of the function is \(100\) which represents the base pay Ryan makes regardless of computer sales.