Question

if a linear function has a \\_\\_\\_\\_\\_\\_\\_\\_ slope, then the graph rises up as \\(x\\) increases.

• zero
• positive

Explanation:

Analyze the definition of slope

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

Determine the sign of the slope

$$ \Delta x > 0 \implies x_2 > x_1 $$

$$ \text{Graph rises up} \implies y_2 > y_1 \implies \Delta y > 0 $$

$$ m = \frac{\Delta y}{\Delta x} > 0 $$

Answer:

• zero
• positive (Correct answer)