Question

a line passes through the points in this table.

x	y
4	1
10	10
16	19
22	28

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 \((4, 1)\) and \((10, 10)\). Here, \( x_1 = 4 \), \( y_1 = 1 \), \( x_2 = 10 \), \( y_2 = 10 \).

Step3: Calculate the slope

Substitute into the formula: \( m=\frac{10 - 1}{10 - 4}=\frac{9}{6}=\frac{3}{2} \). We can verify with another pair, say \((10, 10)\) and \((16, 19)\): \( m=\frac{19 - 10}{16 - 10}=\frac{9}{6}=\frac{3}{2} \), and with \((16, 19)\) and \((22, 28)\): \( m=\frac{28 - 19}{22 - 16}=\frac{9}{6}=\frac{3}{2} \).

Answer:

\(\frac{3}{2}\)