Question

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

Answer 1

Answer:

$\displaystyle y-1=\frac{1}{3}(x+3)$

Step-by-step explanation:

Equation of a Line

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

$\displaystyle y-y_1=\frac{y_2-y_1}{x_2-x_1}(x-x_1)$

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:

$\displaystyle y-1=\frac{4-1}{6+3}(x+3)$

$\displaystyle y-1=\frac{3}{9}(x+3)$

Simplifying:

$\displaystyle y-1=\frac{1}{3}(x+3)$

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

For the point (12,6):

$\displaystyle 6-1=\frac{1}{3}(12+3)$

$\displaystyle 5=\frac{1}{3}(15)$

5=5

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

For the point (30,12):

$\displaystyle 12-1=\frac{1}{3}(30+3)$

$\displaystyle 11=\frac{1}{3}(33)$

11=11

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

Thus, the equation of the line is:

$\mathbf{\displaystyle y-1=\frac{1}{3}(x+3)}$