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Solve for [tex]\( x \)[/tex]:

[tex]\[ 3x = 6x - 2 \][/tex]

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The table below shows the amount that must be repaid, [tex]\( y \)[/tex], when [tex]\( x \)[/tex] dollars are borrowed.

\begin{tabular}{|c|c|}
\hline
Amount Borrowed ([tex]\( x \)[/tex]) & Amount Repaid ([tex]\( y \)[/tex]) \\
\hline
\[tex]$100 & \$[/tex]135 \\
\hline
\[tex]$200 & \$[/tex]260 \\
\hline
\[tex]$500 & \$[/tex]635 \\
\hline
\[tex]$800 & \$[/tex]1010 \\
\hline
\end{tabular}

Which equation represents the relationship?



Answer :

GinnyAnswer
To determine the equation that represents the relationship between the amount borrowed [tex]\( x \)[/tex] and the amount repaid [tex]\( y \)[/tex], we follow these steps:

1. Identify the data points:
We have the following pairs of values from the given table:
[tex]\[ (100, 135), (200, 260), (500, 635), (800, 1010) \][/tex]

2. Assume a linear relationship:
We assume that the relationship between [tex]\( x \)[/tex] and [tex]\( y \)[/tex] can be described by a linear equation of the form:
[tex]\[ y = mx + b \][/tex]
where [tex]\( m \)[/tex] is the slope and [tex]\( b \)[/tex] is the y-intercept.

3. Calculate the slope [tex]\( m \)[/tex]:
The slope [tex]\( m \)[/tex] represents the rate of change of [tex]\( y \)[/tex] with respect to [tex]\( x \)[/tex]. Based on our calculations:
[tex]\[ m = 1.25 \][/tex]

4. Calculate the y-intercept [tex]\( b \)[/tex]:
The y-intercept [tex]\( b \)[/tex] represents the value of [tex]\( y \)[/tex] when [tex]\( x = 0 \)[/tex]. Based on our calculations:
[tex]\[ b = 10 \][/tex]

5. Write the equation:
Substituting the values of [tex]\( m \)[/tex] and [tex]\( b \)[/tex] into the linear equation [tex]\( y = mx + b \)[/tex], we get:
[tex]\[ y = 1.25x + 10 \][/tex]

Therefore, the equation that represents the relationship between the amount borrowed [tex]\( x \)[/tex] and the amount repaid [tex]\( y \)[/tex] is:
[tex]\[ y = 1.25x + 10 \][/tex]

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