Question

at the pascal middle school spring festival, students can use tickets to play a variety of games. the games cost between 1 and 10 tickets. this scatter plot shows the number of tickets different students had left after playing some games at last years festival. the scatter plot also shows the line of best fit. spring festival the equation for the line of best fit is y = -4.2x + 25. according to the equation, which of these statements is true? a student typically started with about 25 tickets. a student typically ran out of tickets after playing 3 or 4 games.

Explanation:

Step1: Analyze the y - intercept

The equation of the line of best fit is in the slope - intercept form \(y = mx + b\), where \(m=-4.2\) is the slope and \(b = 25\) is the y - intercept. When \(x = 0\) (i.e., when no games are played), \(y=-4.2\times0 + 25=25\). This means that on average, students started with about 25 tickets.

Step2: Analyze when tickets run out

Set \(y = 0\) in the equation \(y=-4.2x + 25\). Then \(0=-4.2x + 25\), so \(4.2x=25\), and \(x=\frac{25}{4.2}\approx5.95\). A student typically runs out of tickets after playing about 6 games, not 3 or 4 games.

Answer:

A student typically started with about 25 tickets.