Question
The equation y = 4x represents the relationship between time, x, and distance traveled, y. Which graph represents this relationship?
On a coordinate plane, a line goes through points (0, 40) and (5, 45).
On a coordinate plane, a line goes through points (0, 0) and (1, 4).
On a coordinate plane, a line goes through points (0, 4) and (1, 5).
On a coordinate plane, a line goes through points (0, 4) and (4, 0).
On a coordinate plane, a line goes through points (0, 40) and (5, 45).
On a coordinate plane, a line goes through points (0, 0) and (1, 4).
On a coordinate plane, a line goes through points (0, 4) and (1, 5).
On a coordinate plane, a line goes through points (0, 4) and (4, 0).
Answers
Answered by
GPT-4o mini
To determine which graph represents the equation \( y = 4x \), we can analyze the equation itself.
1. The equation \( y = 4x \) shows that for every unit increase in \( x \), \( y \) increases by 4 units.
2. The line will pass through the origin (0,0) because when \( x = 0 \), \( y \) will also be 0.
Now let's analyze the provided options:
1. **Graph with points (0, 40) and (5, 45)**: This line does not start at the origin and has a steep slope, but does not represent the equation \( y = 4x \).
2. **Graph with points (0, 0) and (1, 4)**: This line begins at the origin (0, 0) and reaches (1, 4), which corresponds to an increase of \( y \) by 4 when \( x \) increases by 1. This matches the equation \( y = 4x \).
3. **Graph with points (0, 4) and (1, 5)**: This line starts above the origin and has a slope of 1, which does not correspond to the equation \( y = 4x \).
4. **Graph with points (0, 4) and (4, 0)**: This graph also does not start at the origin and has a negative slope, which is not consistent with \( y = 4x \).
The only graph that accurately represents the equation \( y = 4x \) is the one with the points **(0, 0) and (1, 4)**.
1. The equation \( y = 4x \) shows that for every unit increase in \( x \), \( y \) increases by 4 units.
2. The line will pass through the origin (0,0) because when \( x = 0 \), \( y \) will also be 0.
Now let's analyze the provided options:
1. **Graph with points (0, 40) and (5, 45)**: This line does not start at the origin and has a steep slope, but does not represent the equation \( y = 4x \).
2. **Graph with points (0, 0) and (1, 4)**: This line begins at the origin (0, 0) and reaches (1, 4), which corresponds to an increase of \( y \) by 4 when \( x \) increases by 1. This matches the equation \( y = 4x \).
3. **Graph with points (0, 4) and (1, 5)**: This line starts above the origin and has a slope of 1, which does not correspond to the equation \( y = 4x \).
4. **Graph with points (0, 4) and (4, 0)**: This graph also does not start at the origin and has a negative slope, which is not consistent with \( y = 4x \).
The only graph that accurately represents the equation \( y = 4x \) is the one with the points **(0, 0) and (1, 4)**.