Question

Find the equation of the linear function represented by the table below in slope- intercept form. x 1 2 3 4 y 1 6 11 16

Answer 1

To find the equation of a line we need to use the formula:

`y-y_1=m(x-x_1)`

Where m is the slope and (x1,y1) is a point on the line. The slope is given by:

`m=(y_2-y_1)/(x_2-x_1)`

Then, the slope of the line (using the first two points on the table) is:

`m=(6-1)/(2-1)=(5)/(1)=5`

Then, the equation of the line is:

`\begin{gathered} y-1=5(x-1) \\ y-1=5x-5 \\ y=5x-5+1 \\ y=5x-4 \end{gathered}`

Therefore, the line is:

`y=5x-4`