Question

1. write an algebraic equation for the following table:

x	y
2	12
7	22
6	20

Explanation:

Step1: Find the slope (m)

We use two points, say \((2, 12)\) and \((6, 20)\). The slope formula is \(m=\frac{y_2 - y_1}{x_2 - x_1}\).
\(m=\frac{20 - 12}{6 - 2}=\frac{8}{4}=2\)

Step2: Use point - slope form \(y - y_1=m(x - x_1)\)

Using the point \((2, 12)\) and \(m = 2\).
\(y-12 = 2(x - 2)\)

Step3: Simplify the equation

Expand the right - hand side: \(y-12=2x - 4\)
Add 12 to both sides: \(y=2x+8\)
We can check with other points. For \(x = 7\), \(y=2\times7 + 8=14 + 8=22\) (matches the table). For \(x = 11\), \(y=2\times11+8=22 + 8=30\) (matches the table).

Answer:

\(y = 2x+8\)