Question

What is the equation of the line represented by the table below?

x y
-3 1
6 4
12 6
30 12

Answer 1

`\displaystyle y-1=(1)/(3)(x+3)`

Explanation:

Equation of a Line

The equation of a line passing through points (x1,y1) and (x2,y2) can be found as follows:

`\displaystyle y-y_1=(y_2-y_1)/(x_2-x_1)(x-x_1)`

The table shows the relation between x and y. It contains the following points

(-3,1), (6,4), (12,6), (30,12).

Taking the two first points, we find the equation of the line:

`\displaystyle y-1=(4-1)/(6+3)(x+3)`

`\displaystyle y-1=(3)/(9)(x+3)`

Simplifying:

`\displaystyle y-1=(1)/(3)(x+3)`

To ensure the rest of the points belong to the line, we test them:

For the point (12,6):

`\displaystyle 6-1=(1)/(3)(12+3)`

`\displaystyle 5=(1)/(3)(15)`

5=5

Since equality is true, the point belongs to the line.

For the point (30,12):

`\displaystyle 12-1=(1)/(3)(30+3)`

`\displaystyle 11=(1)/(3)(33)`

11=11

Since equality is true, the point belongs to the line.

Thus, the equation of the line is:

`\mathbf{\displaystyle y-1=(1)/(3)(x+3)}`