Question
2. Use the graph the answer the following questions. (3 points) a. The constant of proportionality is . b. Write an equation that represents this graph . c. This is a proportional relationship because the y-intercept is .
the y axis is labeled income in money and the x axis is labeled time in hours (5, 70)
the y axis is labeled income in money and the x axis is labeled time in hours (5, 70)
Answers
Answer
is it across then up or up then across on a graph
Answer
whats the grade I get if I get 31 questions of out 41 correct
Answered by
GPT-4o mini
To analyze the graph you've described and answer the questions, we'll outline the steps assuming there is a linear relationship between the two variables (income and time).
a. **The constant of proportionality**: The constant of proportionality (k) can be calculated using the coordinates of a point on the line. If the point (5, 70) means that for 5 hours, the income is $70, the constant of proportionality can be found as:
\[
k = \frac{\text{income}}{\text{time}} = \frac{70}{5} = 14
\]
So, the constant of proportionality is 14.
b. **The equation that represents this graph**: Since we are dealing with a proportional relationship, the relationship can be expressed in the form of the equation:
\[
y = kx
\]
where \( y \) is the income, \( x \) is the time, and \( k \) is the constant of proportionality. Given \( k = 14 \), the equation that represents this graph is:
\[
y = 14x
\]
c. **This is a proportional relationship because the y-intercept is**: In a true proportional relationship, the y-intercept is zero. This indicates that when there is no time (0 hours), the income (y) is also $0. Therefore, the statement can be completed as:
This is a proportional relationship because the y-intercept is **0**.
To summarize:
- a. The constant of proportionality is **14**.
- b. The equation that represents this graph is **y = 14x**.
- c. This is a proportional relationship because the y-intercept is **0**.
a. **The constant of proportionality**: The constant of proportionality (k) can be calculated using the coordinates of a point on the line. If the point (5, 70) means that for 5 hours, the income is $70, the constant of proportionality can be found as:
\[
k = \frac{\text{income}}{\text{time}} = \frac{70}{5} = 14
\]
So, the constant of proportionality is 14.
b. **The equation that represents this graph**: Since we are dealing with a proportional relationship, the relationship can be expressed in the form of the equation:
\[
y = kx
\]
where \( y \) is the income, \( x \) is the time, and \( k \) is the constant of proportionality. Given \( k = 14 \), the equation that represents this graph is:
\[
y = 14x
\]
c. **This is a proportional relationship because the y-intercept is**: In a true proportional relationship, the y-intercept is zero. This indicates that when there is no time (0 hours), the income (y) is also $0. Therefore, the statement can be completed as:
This is a proportional relationship because the y-intercept is **0**.
To summarize:
- a. The constant of proportionality is **14**.
- b. The equation that represents this graph is **y = 14x**.
- c. This is a proportional relationship because the y-intercept is **0**.
Answered by
GPT-4o mini
On a Cartesian graph, the orientation you use to plot points usually depends on whether you are moving along the x-axis (horizontal) or the y-axis (vertical).
When considering the movements “across” and “up,” it refers to how you graphically represent a point using the x and y coordinates:
1. **Across then up**: This means you first move along the x-axis (horizontal) to reach the x-coordinate, and then you move up the y-axis (vertical) to reach the y-coordinate.
For example, if you wanted to plot the point (5, 70):
- First, move **across** to the right to **5** on the x-axis.
- Then, move **up** to **70** on the y-axis.
2. **Up then across**: This is not the common way to represent points on a standard Cartesian graph. You would typically not move up the y-axis first to find the x-coordinate.
In summary, the standard method is to move **across on the x-axis first**, then **up on the y-axis** to plot a point.
When considering the movements “across” and “up,” it refers to how you graphically represent a point using the x and y coordinates:
1. **Across then up**: This means you first move along the x-axis (horizontal) to reach the x-coordinate, and then you move up the y-axis (vertical) to reach the y-coordinate.
For example, if you wanted to plot the point (5, 70):
- First, move **across** to the right to **5** on the x-axis.
- Then, move **up** to **70** on the y-axis.
2. **Up then across**: This is not the common way to represent points on a standard Cartesian graph. You would typically not move up the y-axis first to find the x-coordinate.
In summary, the standard method is to move **across on the x-axis first**, then **up on the y-axis** to plot a point.
Answered by
GPT-4o mini
To calculate your grade based on the number of correct answers, you can use the following formula:
\[
\text{Grade} = \left( \frac{\text{Number of Correct Answers}}{\text{Total Number of Questions}} \right) \times 100
\]
In your case, you got 31 out of 41 questions correct.
So,
\[
\text{Grade} = \left( \frac{31}{41} \right) \times 100 \approx 75.61
\]
Therefore, your grade is approximately **75.6%**.
You would typically round this to the nearest whole number, giving you a final grade of **76%**.
\[
\text{Grade} = \left( \frac{\text{Number of Correct Answers}}{\text{Total Number of Questions}} \right) \times 100
\]
In your case, you got 31 out of 41 questions correct.
So,
\[
\text{Grade} = \left( \frac{31}{41} \right) \times 100 \approx 75.61
\]
Therefore, your grade is approximately **75.6%**.
You would typically round this to the nearest whole number, giving you a final grade of **76%**.
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