Question

before beginning guitar lessons, jane already knew how to play 8 songs. she learns 2 new songs each month in her music class. what does the slope mean in this situation? slope = \frac{vertical distance}{horizontal distance} 2 after each, she knows 2 more

Explanation:

In a linear relationship \(y = mx + b\) (where \(y\) is the number of songs, \(x\) is the number of months, \(m\) is the slope, and \(b\) is the \(y\) - intercept), the slope \(m\) represents the rate of change. Here, the \(x\) - axis is labeled "Number of months" and the \(y\) - axis is labeled "Number of songs". The formula for slope \(m=\frac{\text{vertical change (change in }y\text{)}}{\text{horizontal change (change in }x\text{)}}\). Since \(y\) represents the number of songs and \(x\) represents the number of months, the slope of \(2\) means that for each unit increase in \(x\) (each month), there is an increase of \(2\) in \(y\) (the number of songs).

Answer:

After each month, she knows 2 more songs.