Question

1. write an algebraic equation for the following table:

x	y
9	17
20	50
2	-4
6	8

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 \((2, - 4)\) and \((6,8)\). Slope \( m=\frac{y_2 - y_1}{x_2 - x_1}=\frac{8-(-4)}{6 - 2}=\frac{12}{4}=3\).

Step3: Find y - intercept \( b \)

Substitute \( x = 2\), \( y=-4\) and \( m = 3\) into \( y=mx + b\): \(-4=3\times2 + b\), so \( b=-4 - 6=-10\).

Step4: Verify with other points

For \( x = 9\), \( y=3\times9-10 = 27 - 10 = 17\) (matches). For \( x = 20\), \( y=3\times20-10=60 - 10 = 50\) (matches).

Answer:

\( y = 3x-10 \)