Question

1. write an algebraic equation for the following table:

x	y
2	9
7	34
11	54
3	14

Explanation:

Step1: Assume linear equation form

Assume the equation is \( y = mx + b \), where \( m \) is slope and \( b \) is y - intercept.

Step2: Calculate slope using two points

Take points \((2,9)\) and \((3,14)\). Slope \( m=\frac{y_2 - y_1}{x_2 - x_1}=\frac{14 - 9}{3 - 2}=\frac{5}{1}=5\).

Step3: Find y - intercept \( b \)

Substitute \( x = 2\), \( y = 9\) and \( m = 5\) into \( y=mx + b \).
\( 9=5\times2 + b\)
\( 9 = 10 + b\)
\( b=9 - 10=- 1\).

Step4: Verify with other points

For \( x = 7\), \( y=5\times7-1 = 35 - 1=34\) (matches). For \( x = 11\), \( y=5\times11-1=55 - 1 = 54\) (matches).

Answer:

\( y = 5x-1 \)