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Hugo decided to pay [tex]$2 a week to his brother to buy a bicycle. The equation \( y - 10 = -2(x - 10) \) models the amount of money he owes for the bike, where \( x \) is the number of weeks and \( y \) is the amount of money he still needs to pay.

1. How much did the bicycle cost?
\(\$[/tex] \_\_\_\_\_\_\)

2. After how many weeks will Hugo finish paying for the bike?
[tex]\(\_\_\_\_\_\_\)[/tex] weeks

3. Graph the equation [tex]\( y - 10 = -2(x - 10) \)[/tex]

[tex]\[
\begin{tabular}{|l|l|}
\hline
$x$ & $y$ \\
\hline
& \\
\hline
& \\
\hline
\end{tabular}
\][/tex]

Click or tap the graph to plot a point.

Sagot :

GinnyAnswer
Let's solve this step-by-step.

### 1. Determining the Initial Cost of the Bicycle
We start with the equation given:
[tex]\[ y - 10 = -2(x - 10) \][/tex]

To find the initial cost of the bicycle, we need to determine the amount Hugo owed initially, which corresponds to when [tex]\( x = 0 \)[/tex] (the beginning). Substituting [tex]\( x = 0 \)[/tex] into the equation:

[tex]\[ y - 10 = -2(0 - 10) \][/tex]
[tex]\[ y - 10 = -2(-10) \][/tex]
[tex]\[ y - 10 = 20 \][/tex]
[tex]\[ y = 30 \][/tex]

So, the initial cost of the bicycle is [tex]\(\$30\)[/tex].

Answer: The bicycle cost [tex]\(\$30\)[/tex].

### 2. Determining After How Many Weeks Hugo Will Finish Paying for the Bike
To find out when Hugo finishes paying, we need to know when the amount he owes [tex]\( y \)[/tex] becomes 0. Thus, we set [tex]\( y = 0 \)[/tex] and solve for [tex]\( x \)[/tex]:

[tex]\[ 0 - 10 = -2(x - 10) \][/tex]
[tex]\[ -10 = -2(x - 10) \][/tex]
[tex]\[ -10 = -2x + 20 \][/tex]
[tex]\[ -10 - 20 = -2x \][/tex]
[tex]\[ -30 = -2x \][/tex]
[tex]\[ x = 15 \][/tex]

So, Hugo will finish paying for the bike after 15 weeks.

Answer: Hugo will finish paying for the bike after 15 weeks.

### 3. Completing the Graph
We need to plot the points that satisfy the equation [tex]\( y - 10 = -2(x - 10) \)[/tex] on a graph.

Let's create a few points using the equation:

#### Example Points:
- For [tex]\( x = 0 \)[/tex]:
[tex]\[ y - 10 = -2(0 - 10) \][/tex]
[tex]\[ y - 10 = 20 \][/tex]
[tex]\[ y = 30 \][/tex]
[tex]\((0, 30)\)[/tex]

- For [tex]\( x = 10 \)[/tex]:
[tex]\[ y - 10 = -2(10 - 10) \][/tex]
[tex]\[ y - 10 = 0 \][/tex]
[tex]\[ y = 10 \][/tex]
[tex]\((10, 10)\)[/tex]

- For [tex]\( x = 15 \)[/tex]:
[tex]\[ y - 10 = -2(15 - 10) \][/tex]
[tex]\[ y - 10 = -10 \][/tex]
[tex]\[ y = 0 \][/tex]
[tex]\((15, 0)\)[/tex]

Let's fill in the graph with these points:

### Table of Values:
\begin{tabular}{|l|l|}
\hline[tex]$x$[/tex] & [tex]$y$[/tex] \\
\hline 0 & 30 \\
\hline 10 & 10 \\
\hline 15 & 0 \\
\hline
\end{tabular}

With these points, you can plot the line [tex]\( y - 10 = -2(x - 10) \)[/tex]. So, you would start at [tex]\((0, 30)\)[/tex], cross [tex]\((10, 10)\)[/tex], and end at [tex]\((15, 0)\)[/tex].
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