Question
The table below shows how x and y are related.
The table has 2, 4, 6, 8, 10 in the x column and 3, 6, 9, 12, 15 in the y column.
Which graph shows this same relationship between x and y?
A.
The graph has numbers from 0 to 20 in increments of 2 in the x-axis and from 0 to 10 on the y-axis. A straight line connects (0, 0) to (15, 10).
B.
The graph has numbers from 0 to 20 in increments of 2 in the x-axis and from 0 to 10 on the y-axis. A straight line connects (0, 0) to (20, 10).
C.
The graph has numbers from 0 to 10 on the x-axis and from 0 to 20 in increments of 2 in the y-axis. A straight line connects (0, 0) to (10, 15).
D.
The graph has numbers from 0 to 10 on the x-axis and from 0 to 20 in increments of 2 in the y-axis. A straight line connects (0, 0) to (10, 20).
The table has 2, 4, 6, 8, 10 in the x column and 3, 6, 9, 12, 15 in the y column.
Which graph shows this same relationship between x and y?
A.
The graph has numbers from 0 to 20 in increments of 2 in the x-axis and from 0 to 10 on the y-axis. A straight line connects (0, 0) to (15, 10).
B.
The graph has numbers from 0 to 20 in increments of 2 in the x-axis and from 0 to 10 on the y-axis. A straight line connects (0, 0) to (20, 10).
C.
The graph has numbers from 0 to 10 on the x-axis and from 0 to 20 in increments of 2 in the y-axis. A straight line connects (0, 0) to (10, 15).
D.
The graph has numbers from 0 to 10 on the x-axis and from 0 to 20 in increments of 2 in the y-axis. A straight line connects (0, 0) to (10, 20).
Answers
GPT-4o mini
To find which graph accurately represents the relationship between x and y as provided in the table, we first need to determine the nature of this relationship.
From the table:
- When x = 2, y = 3
- When x = 4, y = 6
- When x = 6, y = 9
- When x = 8, y = 12
- When x = 10, y = 15
We can observe that y increases by 3 for every increase of 2 in x, which suggests a linear relationship. The slope (m) of this linear relationship can be calculated as:
\[
m = \frac{\Delta y}{\Delta x} = \frac{3}{2}
\]
This indicates that the equation for the line can be expressed in the form:
\[
y = \frac{3}{2} x
\]
To verify the y-intercept, when \( x = 0 \), \( y \) also equals 0, thus confirming that the line passes through the origin (0,0).
Now we can calculate the value of y for the maximum x values presented by the line.
When \( x = 10 \):
\[
y = \frac{3}{2} (10) = 15
\]
Next, let's analyze the options given:
A. Connects (0, 0) to (15, 10) - **Incorrect**, since (15, 10) doesn't align with our y-values at maximum x=10.
B. Connects (0, 0) to (20, 10) - **Incorrect**, since (20, 10) does not fit the linear relationship we derived.
C. Connects (0, 0) to (10, 15) - **Correct**, this matches the derived equation and maximum x value.
D. Connects (0, 0) to (10, 20) - **Incorrect**, does not align with output values.
Thus, the correct option is **C**, as it accurately represents the relationship between x and y described in the table.
From the table:
- When x = 2, y = 3
- When x = 4, y = 6
- When x = 6, y = 9
- When x = 8, y = 12
- When x = 10, y = 15
We can observe that y increases by 3 for every increase of 2 in x, which suggests a linear relationship. The slope (m) of this linear relationship can be calculated as:
\[
m = \frac{\Delta y}{\Delta x} = \frac{3}{2}
\]
This indicates that the equation for the line can be expressed in the form:
\[
y = \frac{3}{2} x
\]
To verify the y-intercept, when \( x = 0 \), \( y \) also equals 0, thus confirming that the line passes through the origin (0,0).
Now we can calculate the value of y for the maximum x values presented by the line.
When \( x = 10 \):
\[
y = \frac{3}{2} (10) = 15
\]
Next, let's analyze the options given:
A. Connects (0, 0) to (15, 10) - **Incorrect**, since (15, 10) doesn't align with our y-values at maximum x=10.
B. Connects (0, 0) to (20, 10) - **Incorrect**, since (20, 10) does not fit the linear relationship we derived.
C. Connects (0, 0) to (10, 15) - **Correct**, this matches the derived equation and maximum x value.
D. Connects (0, 0) to (10, 20) - **Incorrect**, does not align with output values.
Thus, the correct option is **C**, as it accurately represents the relationship between x and y described in the table.