Question

1. what is the difference between a slope of 0 and a slope that is undefined? be specific!

Explanation:

The slope formula is $m = \frac{y_2 - y_1}{x_2 - x_1}$. For a slope of 0, the numerator ($y_2 - y_1$) is 0 (so the line is horizontal, parallel to the x - axis, e.g., $y = 5$). For an undefined slope, the denominator ($x_2 - x_1$) is 0 (so the line is vertical, parallel to the y - axis, e.g., $x = 3$), and division by zero is undefined.

Answer:

A slope of 0 occurs when the change in y - values ($\Delta y=y_2 - y_1$) is 0 (the line is horizontal, e.g., $y = c$ where $c$ is a constant). An undefined slope occurs when the change in x - values ($\Delta x=x_2 - x_1$) is 0 (the line is vertical, e.g., $x = c$ where $c$ is a constant), as division by zero is undefined in the slope formula $m=\frac{\Delta y}{\Delta x}$.