Question

find the equation of the linear function represented by the table below in slope - intercept form (y = mx + b).

x	0	1	2	3	4
y	-4	-1	2	5	8

Explanation:

Step1: Find the slope (m)

The formula for slope between two points \((x_1, y_1)\) and \((x_2, y_2)\) is \(m=\frac{y_2 - y_1}{x_2 - x_1}\). Using the first two points \((0, - 4)\) and \((1,-1)\), we have \(m=\frac{-1-(-4)}{1 - 0}=\frac{3}{1}=3\).

Step2: Find the y - intercept (b)

The slope - intercept form of a line is \(y=mx + b\). When \(x = 0\), from the table, \(y=-4\). Substituting \(x = 0\), \(y=-4\) and \(m = 3\) into \(y=mx + b\), we get \(-4=3\times0 + b\), so \(b=-4\).

Step3: Write the equation

Substitute \(m = 3\) and \(b=-4\) into the slope - intercept form \(y=mx + b\). We get \(y = 3x-4\).

Answer:

\(y = 3x-4\)