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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).

1 answer

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).