Problem
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.)
Solution
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
