Question

a line passes through the points in this table.

x | y
1 | 8
2 | 15
3 | 22
4 | 29

what is the slope of the line?
write your answer as an integer or simplified fraction.

Explanation:

Step1: Recall slope formula

The slope \( m \) of a line passing through 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 \( (1, 8) \) and \( (2, 15) \), where \( x_1 = 1,y_1 = 8,x_2=2,y_2 = 15 \).

Step3: Calculate the slope

Substitute the values into the slope formula: \( m=\frac{15 - 8}{2 - 1}=\frac{7}{1}=7 \). We can verify with other points, for example, using \( (2,15) \) and \( (3,22) \), \( m=\frac{22 - 15}{3 - 2}=\frac{7}{1} = 7 \), and with \( (3,22) \) and \( (4,29) \), \( m=\frac{29 - 22}{4 - 3}=\frac{7}{1}=7 \).

Answer:

\( 7 \)