The equation y = 4x represents the relationship between time, x, and distance traveled, y. Which graph represents this relationship?

Question

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).

Answer 1

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).