Question

find the equation of the linear function represented by the table below in slope-intercept form.

x	0	1	2	3	4
y	-3	4	11	18	25

Explanation:

Step1: Recall slope-intercept form

The slope - intercept form of a linear equation is \(y = mx + b\), where \(m\) is the slope and \(b\) is the \(y\) - intercept. The \(y\) - intercept occurs when \(x = 0\). From the table, when \(x = 0\), \(y=-3\), so \(b=-3\).

Step2: Calculate the slope \(m\)

The formula for the slope \(m\) between two points \((x_1,y_1)\) and \((x_2,y_2)\) is \(m=\frac{y_2 - y_1}{x_2 - x_1}\). Let's take two points from the table, for example, \((x_1,y_1)=(0, - 3)\) and \((x_2,y_2)=(1,4)\). Then \(m=\frac{4-(-3)}{1 - 0}=\frac{4 + 3}{1}=7\). We can check with another pair of points, say \((1,4)\) and \((2,11)\). \(m=\frac{11 - 4}{2 - 1}=\frac{7}{1}=7\). So the slope \(m = 7\).

Step3: Write the equation

Substitute \(m = 7\) and \(b=-3\) into the slope - intercept form \(y=mx + b\). We get \(y = 7x-3\).

Answer:

\(y = 7x-3\)