Asked by mywha
Question
Use the image to answer the question.
An illustration shows a coordinate plane with 4 quadrants. The x-axis ranges from negative 9 to 9 in one unit increments, and the y-axis ranges from negative 11 to 11 in one unit increments. A line is graphed on the plane. An upward slanting line passes through points plotted at left parenthesis 3 comma 1 right parenthesis, left parenthesis 6 comma 2 right parenthesis, and left parenthesis 9 comma 3 right parenthesis.
Write the equation of the line y=mx through the origin that describes the proportional relationship shown in the graph.
(1 point)
Use the image to answer the question.
An illustration shows a coordinate plane with 4 quadrants. The x-axis ranges from negative 9 to 9 in one unit increments, and the y-axis ranges from negative 11 to 11 in one unit increments. A line is graphed on the plane. An upward slanting line passes through points plotted at left parenthesis 3 comma 1 right parenthesis, left parenthesis 6 comma 2 right parenthesis, and left parenthesis 9 comma 3 right parenthesis.
Write the equation of the line y=mx through the origin that describes the proportional relationship shown in the graph.
(1 point)
Answers
Answered by
mywha
1/3?
Answered by
GPT-4o mini
To determine the equation of the line \( y = mx \) that describes the proportional relationship, we will need to find the slope \( m \) of the line. The slope is calculated by the change in \( y \) divided by the change in \( x \).
From the points given:
- \( (3, 1) \)
- \( (6, 2) \)
- \( (9, 3) \)
We can use any two points. Let's calculate the slope using the first two points \( (3, 1) \) and \( (6, 2) \):
\[
m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{2 - 1}{6 - 3} = \frac{1}{3}
\]
Now we have the slope \( m = \frac{1}{3} \).
Thus, the equation of the line passing through the origin with this slope is:
\[
y = \frac{1}{3}x
\]
So, the final answer is:
\[
y = \frac{1}{3}x
\]
From the points given:
- \( (3, 1) \)
- \( (6, 2) \)
- \( (9, 3) \)
We can use any two points. Let's calculate the slope using the first two points \( (3, 1) \) and \( (6, 2) \):
\[
m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{2 - 1}{6 - 3} = \frac{1}{3}
\]
Now we have the slope \( m = \frac{1}{3} \).
Thus, the equation of the line passing through the origin with this slope is:
\[
y = \frac{1}{3}x
\]
So, the final answer is:
\[
y = \frac{1}{3}x
\]
Answered by
GPT-4o mini
Yes, the slope \( m \) calculated from the points provided is \( \frac{1}{3} \).
To confirm, let's analyze the points more thoroughly:
- The point \( (3, 1) \) indicates when \( x = 3 \), \( y = 1 \).
- The point \( (6, 2) \) indicates when \( x = 6 \), \( y = 2 \).
- The point \( (9, 3) \) indicates when \( x = 9 \), \( y = 3 \).
We'll use the \( (x,y) \) values to confirm the slope:
From \( (3, 1) \) to \( (6, 2) \):
\[
m = \frac{2 - 1}{6 - 3} = \frac{1}{3}
\]
From \( (6, 2) \) to \( (9, 3) \):
\[
m = \frac{3 - 2}{9 - 6} = \frac{1}{3}
\]
Therefore, we consistently find the slope \( m = \frac{1}{3} \).
Thus, the equation of the line that passes through the origin is correctly given as:
\[
y = \frac{1}{3}x
\]
If you have any further questions or need clarification, feel free to ask!
To confirm, let's analyze the points more thoroughly:
- The point \( (3, 1) \) indicates when \( x = 3 \), \( y = 1 \).
- The point \( (6, 2) \) indicates when \( x = 6 \), \( y = 2 \).
- The point \( (9, 3) \) indicates when \( x = 9 \), \( y = 3 \).
We'll use the \( (x,y) \) values to confirm the slope:
From \( (3, 1) \) to \( (6, 2) \):
\[
m = \frac{2 - 1}{6 - 3} = \frac{1}{3}
\]
From \( (6, 2) \) to \( (9, 3) \):
\[
m = \frac{3 - 2}{9 - 6} = \frac{1}{3}
\]
Therefore, we consistently find the slope \( m = \frac{1}{3} \).
Thus, the equation of the line that passes through the origin is correctly given as:
\[
y = \frac{1}{3}x
\]
If you have any further questions or need clarification, feel free to ask!