Question
Choose the graph of this equation. y = 2.5x
A. Graph of a diagonal line on a coordinate plane going up and to the right with x-axis and y-axis. Co-ordinates are (0,0) and (2,5). B. Graph of a diagonal line on a coordinate plane going up and to the right with x-axis and y-axis. Co-ordinates are (0,0) and (6,6). C. Graph of a diagonal line on a coordinate plane going up and to the right with x-axis and y-axis. Co-ordinates are (0,0) and (6,2). D. Graph of a diagonal line on a coordinate plane going up and to the right with x-axis and y-axis. Co-ordinates are (0,0) and (6,2).
A. Graph of a diagonal line on a coordinate plane going up and to the right with x-axis and y-axis. Co-ordinates are (0,0) and (2,5). B. Graph of a diagonal line on a coordinate plane going up and to the right with x-axis and y-axis. Co-ordinates are (0,0) and (6,6). C. Graph of a diagonal line on a coordinate plane going up and to the right with x-axis and y-axis. Co-ordinates are (0,0) and (6,2). D. Graph of a diagonal line on a coordinate plane going up and to the right with x-axis and y-axis. Co-ordinates are (0,0) and (6,2).
Answers
GPT-4o mini
To determine the correct graph for the equation \( y = 2.5x \), we need to understand what the equation represents.
The equation \( y = 2.5x \) is a linear equation. The slope is 2.5, which means for every unit increase in \( x \), \( y \) increases by 2.5 units. The graph will pass through the origin (0,0).
Let's calculate a few points to see where this line will go:
1. When \( x = 0 \):
\[
y = 2.5(0) = 0 \quad \text{(Point: (0,0))}
\]
2. When \( x = 1 \):
\[
y = 2.5(1) = 2.5 \quad \text{(Point: (1,2.5))}
\]
3. When \( x = 2 \):
\[
y = 2.5(2) = 5 \quad \text{(Point: (2,5))}
\]
4. When \( x = 6 \):
\[
y = 2.5(6) = 15 \quad \text{(Point: (6,15))}
\]
Now we analyze the given options:
- **Option A:** Co-ordinates (0,0) and (2,5) is consistent with our calculations. The point (2,5) is exactly where the line should go since when \( x=2 \), \( y=5 \).
- **Option B:** Co-ordinates (0,0) and (6,6) do not match the line \( y = 2.5x \) since for \( x=6 \), \( y \) should be 15.
- **Option C:** Co-ordinates (0,0) and (6,2) also do not match, as \( y \) should be 15 when \( x=6 \).
- **Option D:** Co-ordinates (0,0) and (6,2) again do not match for the same reason as Option C.
Therefore, the correct graph of the equation \( y = 2.5x \) is:
**A. Graph of a diagonal line on a coordinate plane going up and to the right with x-axis and y-axis. Co-ordinates are (0,0) and (2,5).**
The equation \( y = 2.5x \) is a linear equation. The slope is 2.5, which means for every unit increase in \( x \), \( y \) increases by 2.5 units. The graph will pass through the origin (0,0).
Let's calculate a few points to see where this line will go:
1. When \( x = 0 \):
\[
y = 2.5(0) = 0 \quad \text{(Point: (0,0))}
\]
2. When \( x = 1 \):
\[
y = 2.5(1) = 2.5 \quad \text{(Point: (1,2.5))}
\]
3. When \( x = 2 \):
\[
y = 2.5(2) = 5 \quad \text{(Point: (2,5))}
\]
4. When \( x = 6 \):
\[
y = 2.5(6) = 15 \quad \text{(Point: (6,15))}
\]
Now we analyze the given options:
- **Option A:** Co-ordinates (0,0) and (2,5) is consistent with our calculations. The point (2,5) is exactly where the line should go since when \( x=2 \), \( y=5 \).
- **Option B:** Co-ordinates (0,0) and (6,6) do not match the line \( y = 2.5x \) since for \( x=6 \), \( y \) should be 15.
- **Option C:** Co-ordinates (0,0) and (6,2) also do not match, as \( y \) should be 15 when \( x=6 \).
- **Option D:** Co-ordinates (0,0) and (6,2) again do not match for the same reason as Option C.
Therefore, the correct graph of the equation \( y = 2.5x \) is:
**A. Graph of a diagonal line on a coordinate plane going up and to the right with x-axis and y-axis. Co-ordinates are (0,0) and (2,5).**