Question
The equation y = 8.1x models the relationship between the number of hours Alexander works, x, and the dollar amount he earns, y. Which is the graph of the equation y = 8.1x?A coordinate grid with a curved line starting at (1, 8) curving down and to the right passing through (2, 4), (4, 2), and (7, 1)A coordinate grid with a straight line starting at (0, 0) and (1, 8).A coordinate grid with a straight line starting at (0, 2) passing through (2, 4) and (6, 8).
Answers
GPT-4o mini
The equation \( y = 8.1x \) represents a linear relationship between \( x \) and \( y \), where the slope is \( 8.1 \). This means that for every hour Alexander works, he earns $8.10.
To find the correct graph of this linear equation, we should check for the following characteristics:
1. The line should pass through the origin (0,0) because when \( x = 0 \), \( y \) should also be 0.
2. The slope of the line should indicate that for every increase of 1 in \( x \), \( y \) increases by 8.1.
Now, let’s evaluate the options:
1. **Curved line**: This option does not represent a linear equation, so it cannot be correct.
2. **Straight line starting at (0, 0) and passing through (1, 8)**: This option is consistent with the equation \( y = 8.1x \). If \( x = 1 \), then \( y = 8.1 \cdot 1 = 8.1 \), which is very close to 8 (though not matching exactly unless rounded).
3. **Straight line starting at (0, 2)**: This option cannot be correct because the line does not start at the origin.
The best option that matches the expected graph of the equation \( y = 8.1x \) is the second one: **A coordinate grid with a straight line starting at (0, 0) and passing through (1, 8)**.
To find the correct graph of this linear equation, we should check for the following characteristics:
1. The line should pass through the origin (0,0) because when \( x = 0 \), \( y \) should also be 0.
2. The slope of the line should indicate that for every increase of 1 in \( x \), \( y \) increases by 8.1.
Now, let’s evaluate the options:
1. **Curved line**: This option does not represent a linear equation, so it cannot be correct.
2. **Straight line starting at (0, 0) and passing through (1, 8)**: This option is consistent with the equation \( y = 8.1x \). If \( x = 1 \), then \( y = 8.1 \cdot 1 = 8.1 \), which is very close to 8 (though not matching exactly unless rounded).
3. **Straight line starting at (0, 2)**: This option cannot be correct because the line does not start at the origin.
The best option that matches the expected graph of the equation \( y = 8.1x \) is the second one: **A coordinate grid with a straight line starting at (0, 0) and passing through (1, 8)**.