Final answer:
The equation y=6x+4 is linear because it fits the linear form y=mx+b, with a slope of 6 and y-intercept of 4. The equation y=√x is not linear because it contains a square root, making the rate of change of y non-constant.
Step-by-step explanation:
To determine whether each equation is linear or not, we recall that a linear equation can be written in the form y = mx + b, where m represents the slope and b is the y-intercept. Let's analyze the equations one by one:
y = 6x + 4 is indeed a linear equation because it is in the form y = mx + b, where m is 6 and b is 4. Since it has a constant slope and no exponents or functions applied to x, it represents a straight line when graphed.
y = √x is not a linear equation. The square root function applied to x implies that as x changes, the rate of change of y is not constant, which is a requirement for a linear relationship. Therefore, this equation represents a curve, not a straight line.