Question

a line passes through the points in this table.

x	y
19	12
29	17
39	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 given by \( m=\frac{y_2 - y_1}{x_2 - x_1} \).

Step2: Choose two points

Let's take the first two points \((9, 7)\) and \((19, 12)\). Here, \( x_1 = 9 \), \( y_1 = 7 \), \( x_2 = 19 \), \( y_2 = 12 \).

Step3: Calculate slope

Substitute into the formula: \( m=\frac{12 - 7}{19 - 9}=\frac{5}{10}=\frac{1}{2} \). We can verify with other points (e.g., \((19,12)\) and \((29,17)\)): \( \frac{17 - 12}{29 - 19}=\frac{5}{10}=\frac{1}{2} \), which is consistent.

Answer:

\(\frac{1}{2}\)