Question

question 4 points 1

if a linear function has \\_\\_\\_\\_\\_\\_\\_\\_\\_\\_\\_\\_ slope, then the graph is a vertical line.

zero

undefined

Explanation:

Analyze the definition of slope

$$ m = \frac{\Delta y}{\Delta x} = \frac{y_2 - y_1}{x_2 - x_1} $$

Apply to a vertical line

For a vertical line, the \(x\)-coordinates of all points on the line are constant:

$$ x_2 - x_1 = 0 $$

Substituting this into the slope formula yields division by zero:

$$ m = \frac{y_2 - y_1}{0} \implies \text{undefined} $$

Answer:

If a linear function has <blank>undefined</blank> slope, then the graph is a vertical line.

• zero
• undefined (Correct answer)