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

1. How much did the bicycle cost?
[tex]\$ \square[/tex]

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

Graph the equation [tex]y - 10 = -2(x - 10)[/tex]:

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

Click or tap the graph to plot a point.

Sagot :

GinnyAnswer
### Step-by-Step Solution:

#### 1. Determine the cost of the bicycle:
The equation given to model the amount of money Hugo still needs to pay for the bike is:
[tex]\[ y - 10 = -2(x - 10) \][/tex]

First, we need to rearrange this equation to solve for [tex]\( y \)[/tex] in terms of [tex]\( x \)[/tex]:
[tex]\[ y - 10 = -2(x - 10) \][/tex]

Distribute the [tex]\(-2\)[/tex]:
[tex]\[ y - 10 = -2x + 20 \][/tex]

Add 10 to both sides to isolate [tex]\( y \)[/tex]:
[tex]\[ y = -2x + 30 \][/tex]

To find the initial amount Hugo needs to pay (which represents the total cost of the bicycle), we need to determine [tex]\( y \)[/tex] when [tex]\( x = 0 \)[/tex]:
[tex]\[ y = -2(0) + 30 \][/tex]
[tex]\[ y = 30 \][/tex]

So, the bicycle cost:
[tex]\[ \boxed{30} \][/tex]

#### 2. Determine the number of weeks Hugo will finish paying for the bike:
To find the number of weeks it takes for Hugo to finish paying for the bike, we set [tex]\( y \)[/tex] to 0 (the point at which he owes no more money) and solve for [tex]\( x \)[/tex]:
[tex]\[ 0 = -2x + 30 \][/tex]

Rearrange the equation to solve for [tex]\( x \)[/tex]:
[tex]\[ 2x = 30 \][/tex]
[tex]\[ x = 15 \][/tex]

So, Hugo will finish paying for the bike after:
[tex]\[ \boxed{15} \text{ weeks} \][/tex]

#### 3. Populate the table for the graph:
To graph the equation [tex]\( y - 10 = -2(x - 10) \)[/tex], we need points [tex]\( (x, y) \)[/tex] that satisfy the equation. Here are some values:

1. When [tex]\( x = 0 \)[/tex]:
[tex]\[ y = -2(0) + 30 = 30 \][/tex]

2. When [tex]\( x = 5 \)[/tex]:
[tex]\[ y = -2(5) + 30 = 20 \][/tex]

3. When [tex]\( x = 10 \)[/tex]:
[tex]\[ y = -2(10) + 30 = 10 \][/tex]

4. When [tex]\( x = 15 \)[/tex]:
[tex]\[ y = -2(15) + 30 = 0 \][/tex]

So, the table for the graph is:
[tex]\[ \begin{array}{|l|l|} \hline x & y \\ \hline 0 & 30 \\ 5 & 20 \\ 10 & 10 \\ 15 & 0 \\ \hline \end{array} \][/tex]

#### 4. Draw the graph:
Using the table values, you can plot the points [tex]\( (0, 30) \)[/tex], [tex]\( (5, 20) \)[/tex], [tex]\( (10, 10) \)[/tex], and [tex]\( (15, 0) \)[/tex] on the graph. The line that connects these points represents the equation [tex]\( y - 10 = -2(x - 10) \)[/tex].

The graph will be a straight line decreasing from [tex]\( (0, 30) \)[/tex] to [tex]\( (15, 0) \)[/tex].
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