To determine the slope of the line described by the given points in the table, let's follow these steps:
[tex]\[ \begin{tabular}{|c|c|}
\hline
$x$ & $y$ \\
\hline
2 & 1 \\
\hline
4 & 7 \\
\hline
6 & 13 \\
\hline
8 & 19 \\
\hline
\end{tabular} \][/tex]
1. Identify the coordinates:
- The given points are:
- Point 1: [tex]\((2, 1)\)[/tex]
- Point 2: [tex]\((4, 7)\)[/tex]
- Point 3: [tex]\((6, 13)\)[/tex]
- Point 4: [tex]\((8, 19)\)[/tex]
2. Choose any two points to determine the slope:
- We can choose the first two points for simplicity, so we use:
- Point 1: [tex]\((2, 1)\)[/tex]
- Point 2: [tex]\((4, 7)\)[/tex]
3. Calculate the differences in the coordinates:
- Difference in x-coordinates: [tex]\(\Delta x = 4 - 2 = 2\)[/tex]
- Difference in y-coordinates: [tex]\(\Delta y = 7 - 1 = 6\)[/tex]
4. Calculate the slope:
[tex]\[
\text{slope (m)} = \frac{\Delta y}{\Delta x} = \frac{6}{2} = 3.0
\][/tex]
Thus, the slope of the line described by the points in the table is [tex]\(3.0\)[/tex].
