Question

1. write a linear equation for the table.

x | -8 | -2 | 4 | 6
y | 2 | 5 | 8 | 9

Explanation:

Step1: Find the slope (m)

Use two points, e.g., \((-8, 2)\) and \((-2, 5)\). The slope formula is \(m=\frac{y_2 - y_1}{x_2 - x_1}\).
\(m=\frac{5 - 2}{-2 - (-8)}=\frac{3}{6}=\frac{1}{2}\)

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

Using the point \((-8, 2)\) and \(m = \frac{1}{2}\):
\(y - 2=\frac{1}{2}(x - (-8))\)
\(y - 2=\frac{1}{2}(x + 8)\)

Step3: Simplify to slope - intercept form

\(y - 2=\frac{1}{2}x+4\)
\(y=\frac{1}{2}x + 4+2\)
\(y=\frac{1}{2}x+6\)

Answer:

\(y=\frac{1}{2}x + 6\)