Identify the Correct Function: Analyzing 4 Linear Graphs on Coordinate Plane

Choose the appropriate function for the number line 4.

To solve this problem, we need to determine the function that corresponds to the line labeled "4" on the number line.

The line labeled "4" is depicted in orange and appears to pass through the origin, indicating that the y-intercept is 0. Therefore, the equation has the form $y = mx$.

Upon examining this line, we observe that it is direct and passes through the origin at a $45^\circ$ angle to both axes, suggesting that the slope $m$ is 1. This is to say, for each unit increase in $x$, $y$ also increases by the same magnitude.

• The equation thus simplifies to $y = x$.

We next compare our result to the given function choices:

• Choice A: $y = -x$ (Negative slope)
• Choice B: $y = x$ (Positive slope of 1)
• Choice C: $y = 6x$ (Steeper positive slope)
• Choice D: $y = -6x$ (Steeper negative slope)

The line labeled "4" directly matches Choice B, $y = x$, as both the direction and slope align with our observations.

Therefore, the function corresponding to the number line labeled "4" is $y = x$.