Question

Write an equation from write an equation from a table of values

Answer 1

To solve the exercise, you can first graph the points to see if they have a linear relationship, that is, if all the points are on the same line. So, you have

Since the relationship of the points is linear, then you can take two of the points through which the line passes, find the slope of the line, and then use the formula point-slope.

The formula for the slope is

`\begin{gathered} m=(y_(2)-y_(1))/(x_(2)-x_(1)) \\ \text{ Where m is the slope of the line and} \\ (x_1,y_1),(x_2,y_2)\text{ are two points through which the line passes} \end{gathered}`

If for example, you take the points

`\begin{gathered} (x_1,y_1)=(2,9) \\ (x_2,y_2)=(6,-7) \end{gathered}`

You have

`\begin{gathered} m=(-7-9)/(6-2) \\ m=(-16)/(4) \\ m=-4 \end{gathered}`

Now using the formula point-slope, that is,

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

You have

`\begin{gathered} y-9_{}=-4(x-2_{}) \\ y-9_{}=-4x-4\cdot-2 \\ y-9_{}=-4x+6 \\ \text{ Add 9 }to\text{ both sides of the equation} \\ y-9+9=-4x+6+9 \\ y=-4x+17 \end{gathered}`

Therefore, the equation representing the values ​​in the table is

`y=-4x+17`