Question

harper is knitting a scarf for her cousins birthday. she plans to knit every night, making the scarf 5 centimeters longer each night. write an equation that shows the relationship between the number of nights harper spends knitting, x, and the length of the scarf in centimeters, y. y =

Explanation:

Step1: Identify the relationship type

This is a linear relationship where the length of the scarf increases by a constant amount (5 cm) each night. The general form of a linear equation is \( y = mx + b \), where \( m \) is the slope (rate of change) and \( b \) is the y - intercept. Since we assume the scarf starts at length 0 (before any knitting nights), \( b = 0 \).

Step2: Determine the slope (m)

The rate of change (slope) \( m \) is 5, because the length of the scarf increases by 5 centimeters each night. So substituting \( m = 5 \) and \( b = 0 \) into the linear equation \( y=mx + b \), we get \( y = 5x+0 \), which simplifies to \( y = 5x \).

Answer:

\( 5x \) (or \( y = 5x \) when considering the full equation format for the boxed answer as per the problem's requirement of filling \( y=\) with the right - hand side expression)