Question

Michelle will sell her homemade necklaces for $8 each at a craft fair. It costs her $150 for the booth rental at the craft fair.

She made 200 necklaces to sell.
Part B Michelle wants to graph the equation for her profit from selling her necklaces. The y-intercept of this graph will be
her profit from selling none of her necklaces.
What is the y-intercept of the graph of the equation that represents Michelle's profit from selling her necklaces?

Answer 1

The y-intercept is y = -$150

Explanation:

We know that:

Each necklace is sold for $8.

The total cost for Michelle is $150.

The profit equation is:

Profit = Revenue - Cost.

We already know that Cost = $150

The revenue will depend on x, the number of necklaces sold, so if each one costs $8, and she sells x of them, the revenue is:

Revenue = $8*x

Then the profit, as a function of x, is:

y = P(x) = $8*x - $150

Where y represents the profit.

Now we want to find the y-intercept of the profit equation, where the y-intercept is the y-value when we use x = 0

Then the y-intercept is:

P(0) = $8*0 - $150 = -$150

Also the graph of the equation can be seen below, where you need to remember that x can be any value in [0, 200] and only can be an integer.

So you only need to graph the line between x = 0 and x = 200.