Final answer:
Equations A) 2x + 3y = 6, B) y = 5, D) y = 10 - x, and F) y = -x represent relationships where y is a linear function of x, as they can be rearranged into the form y = mx + b.
Step-by-step explanation:
To determine which equations represent a linear function of x, we should look for equations that can be written in the form y = mx + b, where m represents the slope and b represents the y-intercept. Based on this, we can evaluate the given options:
A) 2x + 3y = 6: This can be rearranged to y = -⅓x + 2, which is linear.
B) y = 5: This equation represents a horizontal line, which is a special case of a linear equation with a slope of 0.
C) x = 1: This is not a function of x as y is not dependent on x. It represents a vertical line.
D) y = 10 - x: This can be rewritten as y = -x + 10, that is linear.
E) y = x² + 5x + 6: This is a quadratic function, not linear because of the x² term.
F) y = -x: This is linear and can be written as y = -1x + 0.
Thus, equations A, B, D, and F are the ones where y is a linear function of x.