Question

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

Explanation:

Step1: Recall the slope formula

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

Step2: Substitute the given slope and \( \Delta x \)

We know that the slope \( m = 1 \) and \( \Delta x=1 \) (since \( x \) increases by 1). Substituting into the slope formula \( 1=\frac{\Delta y}{1} \).

Step3: Solve for \( \Delta y \)

Multiplying both sides of the equation \( 1=\frac{\Delta y}{1} \) by 1, we get \( \Delta y = 1 \).

Answer:

1