Question

tyshawn borrowed some money from his friend in order to help buy a new video game system. tyshawn agreed to pay the friend back some amount every week until his loan was paid off. let ( l ) represent the amount tyshawn owes his friend after ( t ) weeks. the table below has select values showing the linear relationship between ( t ) and ( l ). determine how many weeks when the amount of money tyshawn owed his friend was $30.

( t )	( l )
6	60
9	15

Explanation:

Step1: Find the slope of the linear function

The slope \( m \) between two points \((t_1, L_1)\) and \((t_2, L_2)\) is given by \( m=\frac{L_2 - L_1}{t_2 - t_1} \). Using the points \((3, 105)\) and \((6, 60)\):
\( m=\frac{60 - 105}{6 - 3}=\frac{- 45}{3}=- 15 \)

Step2: Find the equation of the line

Using the point - slope form \( L - L_1=m(t - t_1) \), with the point \((3, 105)\) and \( m=-15 \):
\( L - 105=-15(t - 3) \)
\( L - 105=-15t + 45 \)
\( L=-15t + 150 \)

Step3: Solve for \( t \) when \( L = 30 \)

Substitute \( L = 30 \) into the equation \( L=-15t + 150 \):
\( 30=-15t+150 \)
Subtract 150 from both sides: \( 30 - 150=-15t \)
\( - 120=-15t \)
Divide both sides by - 15: \( t=\frac{-120}{-15}=8 \)

Answer:

8