Model the data in the table with a linear equation in slope-intercept form. Then tell what the slope and $y$-intercept represent.
\begin{tabular}{|c|c|}
\hline \begin{tabular}{c}
Time Worked, \\
$\mathrm{x}(\mathrm{h})$
\end{tabular} & \begin{tabular}{c}
Wages Earned, \\
$\mathrm{y}(\$)$
\end{tabular} \\
\hline 1 & 8.50 \\
\hline 3 & 25.50 \\
\hline 6 & 51.00 \\
\hline 9 & 76.50 \\
\hline
\end{tabular}
Write the linear equation in slope-intercept form.
\[
y=
\]
(Use integers or decimals for any numbers in the expression.)
Answer
\(\boxed{y = 8.5x + 0}\) or simply \(\boxed{y = 8.5x}\) is the linear equation in slope-intercept form
Step 1 ：Calculate the slope (m) using the formula \(m = \frac{y2 - y1}{x2 - x1}\). Using the points (1, 8.50) and (3, 25.50), we get \(m = \frac{25.50 - 8.50}{3 - 1} = \frac{17}{2} = 8.5\)
Step 2 ：Find the y-intercept (b) using the formula \(y = mx + b\). Using the point (1, 8.50) and the slope 8.5, we get \(8.50 = 8.5 * 1 + b\), which simplifies to \(b = 8.50 - 8.5 = 0\)
Step 3 ：\(\boxed{y = 8.5x + 0}\) or simply \(\boxed{y = 8.5x}\) is the linear equation in slope-intercept form
