Question

complete the sentence with increases or decreases.

if a line has positive slope, then as \\(x\\) increases, \\(y\\) select.

options:

• increases
• decreases

Explanation:

Define slope of a line

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

Analyze positive slope condition

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

Determine behavior of y as x increases

$$ \Delta x > 0 \implies \Delta y > 0 $$

Answer:

Complete the sentence with increases or decreases.

If a line has positive slope, then as \(x\) increases, \(y\) <blank>increases</blank>.