Question

Fill in the missing numbers to complete the linear equation that gives the rule for this table.x: 0, 1, 2, 3y: 3, 17, 31, 45Y = ?x + ?

Answer 1

y = 14x + 3

Step-by-step explanation

We have the table that gives the values of x and y.

We want to find the linear equation that describes the data.

The general form of a linear equation is:

y = mx + c

where m = slope

c = intercept

So, we have to find the slope of the equation first.

We do that by using:

`m\text{ = }\frac{y2\text{ - y1}}{x2\text{ - x1}}`

where (x1, y1) and (x2, y2) are two sets of data from the table.

Let us pick (x1, y1) as (0, 3) and (x2, y2) as (2, 31)

So, we have that:

`\begin{gathered} m\text{ = }\frac{31\text{ - 3}}{2\text{ - 0}} \\ m\text{ = }(28)/(2) \\ m\text{ = 14} \end{gathered}`

Now, we use the point-slope method to find the equation:

y - y1 = m(x - x1)

=> y - 3 = 14(x - 0)

y - 3 = 14x

=> y = 14x + 3

That is the equation.