Question

the points in the table lie on a line. find the slope of the line. \\(\

$$\begin{array}{|c|c|c|c|c|}\\hline x & -3 & 2 & 7 & 12 \\\\ \\hline y & 0 & 2 & 4 & 6 \\\\ \\hline \\end{array}$$

\\) the slope is \\(\square\\).

Explanation:

Step1: Recall slope formula

The slope \( m \) between two points \( (x_1, y_1) \) and \( (x_2, y_2) \) is \( m=\frac{y_2 - y_1}{x_2 - x_1} \).

Step2: Choose two points

Let's take the first two points \( (-3, 0) \) and \( (2, 2) \). Here, \( x_1=-3 \), \( y_1 = 0 \), \( x_2=2 \), \( y_2=2 \).

Step3: Calculate slope

Substitute into the formula: \( m=\frac{2 - 0}{2 - (-3)}=\frac{2}{5} \). We can check with other points, e.g., \( (2,2) \) and \( (7,4) \): \( m=\frac{4 - 2}{7 - 2}=\frac{2}{5} \), which is consistent.

Answer:

\(\frac{2}{5}\)