Question

a line passes through the points in this table.

x	y
4	9
12	-9
20	-27
28	-45

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

Let's take the first two points \((4, 9)\) and \((12, -9)\). Here, \( x_1 = 4 \), \( y_1 = 9 \), \( x_2 = 12 \), \( y_2 = -9 \).

Step3: Calculate slope

Substitute into the formula: \( m = \frac{-9 - 9}{12 - 4} = \frac{-18}{8} = -\frac{9}{4} \)? Wait, no, wait, let's check with another pair. Let's take \((12, -9)\) and \((20, -27)\). Then \( m = \frac{-27 - (-9)}{20 - 12} = \frac{-18}{8} = -\frac{9}{4} \)? Wait, no, wait, 20 - 12 is 8, -27 - (-9) is -18. Wait, but let's take first and third: (4,9) and (20,-27). \( m = \frac{-27 - 9}{20 - 4} = \frac{-36}{16} = -\frac{9}{4} \)? Wait, no, 20 - 4 is 16, -27 -9 is -36. Simplify: -36/16 = -9/4? Wait, but wait, let's check the x differences: 12 -4 =8, 20 -12=8, 28 -20=8. So x increases by 8 each time. y differences: -9 -9 = -18, -27 - (-9) = -18, -45 - (-27) = -18. So y decreases by 18 each time x increases by 8. So slope is -18/8 = -9/4? Wait, no, -18 divided by 8 is -9/4? Wait, 18 divided by 2 is 9, 8 divided by 2 is 4. So yes, -9/4. Wait, but let's do it with (4,9) and (12,-9): \( m = \frac{-9 - 9}{12 - 4} = \frac{-18}{8} = -\frac{9}{4} \). Yep, that's correct.

Answer:

\(-\frac{9}{4}\)