Question

a line passes through the points in this table.

x	y
2	7
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 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 \((2, 7)\) and \((3, 12)\). Here, \( x_1 = 2 \), \( y_1 = 7 \), \( x_2 = 3 \), \( y_2 = 12 \).

Step3: Calculate the slope

Substitute the values into the slope formula: \( m=\frac{12 - 7}{3 - 2}=\frac{5}{1}=5 \). We can verify with other points, e.g., \((3,12)\) and \((4,17)\): \( \frac{17 - 12}{4 - 3}=\frac{5}{1}=5 \), and \((4,17)\) and \((5,22)\): \( \frac{22 - 17}{5 - 4}=\frac{5}{1}=5 \). So the slope is consistent.

Answer:

5