Question

1. if the slope of a linear function is 0, what does that mean?

a. y always goes up
b. y always goes down
c. y equals x
d. y never changes

Explanation:

The slope of a linear function is calculated as \( \frac{\Delta y}{\Delta x} \) (change in y over change in x). If the slope is 0, then \( \Delta y = 0 \) (since \( \frac{0}{\Delta x}=0 \) for \( \Delta x
eq0 \)). A change in y of 0 means the y - value does not change as x changes.

• Option a: If y always goes up, the slope would be positive, not 0.
• Option b: If y always goes down, the slope would be negative, not 0.
• Option c: If \( y = x \), the slope is 1 (since \( y=x\) can be written as \( y = 1x+0\)), not 0.
• Option d: If y never changes, \( \Delta y = 0 \), so the slope \( \frac{\Delta y}{\Delta x}=0 \) (for \( \Delta x

eq0 \)), which matches a slope of 0.

Answer:

d. y never changes