Question
use the image described to answer the question.
A graph shows a horizontal axis representing time in days ranging from 0 to 10 in increments of 1. The vertical axis represents cookies in a jar ranging from 0 to 10 in increments of 1. Two plotted points are: left parenthesis 1 comma 6 right parenthesis, left parenthesis 2 comma 5 right parenthesis. These points are joined by a straight line with arrows on both the ends; the straight line continues beyond the two points until it intercepts the horizontal axis and the vertical axis.
interpret the y-intercept and slope in the context of this situation. For the slope, give the most simplified rate using whole numbers.
the y-intercept is _ cookie(s). The slope is _ cookie(s) every _ day(s).
A graph shows a horizontal axis representing time in days ranging from 0 to 10 in increments of 1. The vertical axis represents cookies in a jar ranging from 0 to 10 in increments of 1. Two plotted points are: left parenthesis 1 comma 6 right parenthesis, left parenthesis 2 comma 5 right parenthesis. These points are joined by a straight line with arrows on both the ends; the straight line continues beyond the two points until it intercepts the horizontal axis and the vertical axis.
interpret the y-intercept and slope in the context of this situation. For the slope, give the most simplified rate using whole numbers.
the y-intercept is _ cookie(s). The slope is _ cookie(s) every _ day(s).
Answers
GPT-4o mini
To interpret the graph in the context of the situation regarding cookies in a jar over time:
1. **Y-Intercept**: The y-intercept occurs when time (x) is 0. You would need to find the value of cookies (y) at this point. Based on the line that extends from the two points (1, 6) and (2, 5), we can extrapolate to find the y-intercept. If the line decreases by 1 cookie for every day (as inferred from the two points given), we can estimate that at time 0, there would be 7 cookies in the jar.
Therefore, the y-intercept is **7 cookie(s)**.
2. **Slope**: The slope can be calculated using the two points provided: (1, 6) and (2, 5). The change in cookies (y) over the change in days (x) is:
\[
\text{slope} = \frac{y_2 - y_1}{x_2 - x_1} = \frac{5 - 6}{2 - 1} = \frac{-1}{1} = -1
\]
This indicates that the number of cookies decreases by 1 for every 1 day.
Therefore, the slope is **1 cookie(s) every 1 day(s)**.
Putting it all together:
The y-intercept is **7 cookie(s)**. The slope is **1 cookie(s) every 1 day(s)**.
1. **Y-Intercept**: The y-intercept occurs when time (x) is 0. You would need to find the value of cookies (y) at this point. Based on the line that extends from the two points (1, 6) and (2, 5), we can extrapolate to find the y-intercept. If the line decreases by 1 cookie for every day (as inferred from the two points given), we can estimate that at time 0, there would be 7 cookies in the jar.
Therefore, the y-intercept is **7 cookie(s)**.
2. **Slope**: The slope can be calculated using the two points provided: (1, 6) and (2, 5). The change in cookies (y) over the change in days (x) is:
\[
\text{slope} = \frac{y_2 - y_1}{x_2 - x_1} = \frac{5 - 6}{2 - 1} = \frac{-1}{1} = -1
\]
This indicates that the number of cookies decreases by 1 for every 1 day.
Therefore, the slope is **1 cookie(s) every 1 day(s)**.
Putting it all together:
The y-intercept is **7 cookie(s)**. The slope is **1 cookie(s) every 1 day(s)**.