Question

1. write an algebraic equation for the following table:

x	y
3	1
9	19
1	-5
5	7

Explanation:

Step1: Assume linear equation form

Assume the equation is \( y = mx + b \), where \( m \) is the slope and \( b \) is the y - intercept.
Take two points, say \( (x_1,y_1)=(3,1) \) and \( (x_2,y_2)=(1, - 5) \).
The formula for slope \( m=\frac{y_2 - y_1}{x_2 - x_1} \).
Substitute the values: \( m=\frac{-5 - 1}{1 - 3}=\frac{-6}{-2}=3 \).

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

Use the point \( (x = 3,y = 1) \) and \( m = 3 \) in \( y=mx + b \).
\( 1=3\times3 + b \)
\( 1 = 9 + b \)
Subtract 9 from both sides: \( b=1 - 9=-8 \).

Step3: Verify the equation

Check with another point, say \( (x = 5,y = 7) \).
Left - hand side (LHS): \( y = 7 \)
Right - hand side (RHS): \( 3x-8=3\times5 - 8=15 - 8 = 7 \).
Check with \( (x = 9,y = 19) \): \( 3\times9-8=27 - 8 = 19 \).
Check with \( (x = 1,y=-5) \): \( 3\times1-8=3 - 8=-5 \).

Answer:

\( y = 3x-8 \)