Question

interpreting a graph y - intercept and slope

1. the cost of cookies at a bakery is shown on the graph, x represents the number of cookies and y represents the total cost.

a. what is the meaning of the y - intercept?
b. what is the meaning of the slope(rate of change)?

1. john is planning on saving some money every week, x represents the weeks and y represents the total savings.

a. what is the meaning of the y - intercept?
b. what is the meaning of the slope(rate of change)?

Explanation:

1. Cookies Cost Graph

a. Y - intercept

• Step1: Recall Y - intercept definition

The Y - intercept is the value of \(y\) when \(x = 0\). In the context of the cost of cookies (\(x\) is the number of cookies, \(y\) is the cost), when \(x=0\) (no cookies are bought), the \(y\) - value represents the base cost or a fixed cost (maybe an entrance fee or a packaging cost that is charged even if no cookies are bought).

b. Slope (Rate of change)

• Step1: Recall slope formula and meaning

The slope \(m=\frac{\Delta y}{\Delta x}\). In this cost - cookie context, \(\Delta y\) is the change in cost and \(\Delta x\) is the change in the number of cookies. So, the slope represents the cost per cookie. For example, if the slope is \(2\), it means that for each additional cookie, the cost increases by \(2\) units (say, dollars).

2. John's Savings Graph

a. Y - intercept

• Step1: Recall Y - intercept definition

The Y - intercept is the value of \(y\) when \(x = 0\). In the context of John's savings (\(x\) is the number of weeks, \(y\) is the total savings), when \(x = 0\) (at the start, before any weeks of saving have passed), the \(y\) - value represents the initial amount of money John had before he started saving regularly.

b. Slope (Rate of change)

• Step1: Recall slope formula and meaning

The slope \(m=\frac{\Delta y}{\Delta x}\). In the savings - weeks context, \(\Delta y\) is the change in savings and \(\Delta x\) is the change in the number of weeks. So, the slope represents the amount of money John saves per week. For example, if the slope is \(5\), it means that John saves \(5\) units (say, dollars) each week.

Answer:

1.
a. The \(y\) - intercept represents the fixed cost (cost when no cookies are bought).
b. The slope represents the cost per cookie.
2.
a. The \(y\) - intercept represents the initial amount of money John had before he started saving.
b. The slope represents the amount of money John saves per week.