Question

Determine an equation for a function with the following table of valuesXу6137168199221025

Answer 1

The equation in the table is linear because as the x values increase by 1, and y values increase by 3.

The general form of a linear equation is :

`y\text{ = ax + b}`

where:

a is the slope and b is the intercept

The slope can be calculated using the fomula:

`slope\text{ =}(y_2-y_1)/(x_2-x_1)\text{ }`

where (x1,y1) and (x2,y2) are two points on the table.

We can find two points on the table:

(6, 13) and (7, 16)

Hence, the slope:

`\begin{gathered} \text{slope = }(16-13)/(7-6) \\ =\text{ 3} \end{gathered}`

The intercept is the value of y when the line cuts the y-axis.

Using the formula for slope and the point (0,y), we can find the intercept.

`\begin{gathered} (y-13)/(0-6)=3 \\ -18\text{ = y-13} \\ y\text{ = -18 + 13} \\ =\text{ -5} \end{gathered}`

Hence, the required equation is:

`y\text{ = 3x - 5}`

Answer:

y = 3x - 5