Question

a line passes through the points in this table.

x	y
3	12
4	17
5	22

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

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

Take the first two points \( (2, 7) \) and \( (3, 12) \), where \( x_1 = 2 \), \( y_1 = 7 \), \( x_2 = 3 \), \( y_2 = 12 \).

Step3: Calculate slope

Substitute into the formula: \( m=\frac{12 - 7}{3 - 2}=\frac{5}{1}=5 \). We can verify with other points (e.g., \( (3,12) \) and \( (4,17) \)): \( \frac{17 - 12}{4 - 3}=\frac{5}{1}=5 \), which confirms the slope.

Answer:

\( 5 \)