Question

1. write an algebraic equation for the following table

x	y
3	-3
8	7
5	1

Explanation:

Step1: Check the relationship between x and y

Let's assume the equation is in the form \( y = mx + b \). Take two points, say (10, 11) and (3, -3). First, calculate the slope \( m \):
\( m=\frac{y_2 - y_1}{x_2 - x_1}=\frac{-3 - 11}{3 - 10}=\frac{-14}{-7} = 2 \)

Step2: Find the y - intercept \( b \)

Use the point (10, 11) and \( m = 2 \) in \( y=mx + b \):
\( 11=2\times10 + b \)
\( 11 = 20 + b \)
\( b=11 - 20=-9 \)

Step3: Verify with other points

Check (8, 7): \( y = 2\times8-9=16 - 9 = 7 \), which matches. Check (5, 1): \( y = 2\times5-9 = 10 - 9 = 1 \), which also matches. So the equation is \( y = 2x-9 \)

Answer:

\( y = 2x - 9 \)