Question

a line with a slope of 1 means that for every increase of 1 in x, y increases by ______.

Explanation:

Step1: Recall slope definition

The slope \( m \) of a line is defined as \( m = \frac{\Delta y}{\Delta x} \), where \( \Delta y \) is the change in \( y \) and \( \Delta x \) is the change in \( x \).

Step2: Substitute slope value

Given \( m = 1 \) and \( \Delta x = 1 \) (increase of 1 in \( x \)), substitute into the slope formula: \( 1=\frac{\Delta y}{1} \). Solving for \( \Delta y \), we get \( \Delta y = 1\times1 = 1 \).

Answer:

1