Questions: Jamal wants to buy a new game system that costs 200. He does not have enough money to buy it today, so he compares layaway plans at different stores. The Plan at Store A is shown on the graph.
Store B requires an initial payment of 60 and weekly payments of 20 until the balance is paid in full.
Write an equation in slope-Intercept form for Store A's layaway plan. Let x represent number of weeks and y represent balance owed.
y = -20x + 140
Transcript text: Jamal wants to buy a new game system that costs $\$ 200$. He does not have enough money to buy it today, so he compares layaway plans at different stores. The Plan at Store $A$ is shown on the graph.
Store $B$ requires an initial payment of $\$ 60$ and weekly payments of $\$ 20$ until the balance is paid in full.
Write an equation in slope-Intercept form for Store A's layaway plan. Let $x$ represent number of weeks and $y$ represent balance owed.
\[
y=-20 x+140
\]
Solution
Solution Steps
Step 1: Determine the initial payment for Store B.
The problem states that Store B requires an initial payment of $60. This represents the y-intercept of the equation, which is the balance owed when the number of weeks is 0.
Step 2: Determine the weekly payment for Store B.
The problem states that Store B requires weekly payments of $20. This represents the slope of the equation, which is the rate at which the balance owed decreases per week. Since the balance decreases, the slope is negative.
Step 3: Write the equation in slope-intercept form.
The slope-intercept form of a linear equation is \(y = mx + b\), where \(m\) is the slope and \(b\) is the y-intercept. In this case, the slope \(m\) is -20 and the y-intercept \(b\) is 60. Therefore, the equation for Store B's layaway plan is: