Question

the points in the table lie on a line. find the slope of the line.
x | -3 | 2 | 7 | 12
y | 0 | 2 | 4 | 6
the slope is \square.

Explanation:

Step1: Recall the slope formula

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

Step2: Choose two points from the table

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 the slope

Substitute the values into the slope formula: \( m=\frac{2 - 0}{2-(-3)}=\frac{2}{2 + 3}=\frac{2}{5} \). We can verify with another pair, say \( (2, 2) \) and \( (7, 4) \). Then \( m=\frac{4 - 2}{7 - 2}=\frac{2}{5} \), which is the same.

Answer:

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