Question

What is the equation of the line for this function? (0, 0), (2, 1), (4, 2), (6, 3).

Answer 1

The equation of the line is $y=\frac{1}{2}x$

Explanation:

Given that the set of ordered pairs is (0,0), (2,1), (4,2), (6,3)

We need to determine the equation of the line.

Slope:

The slope of the line can be determined using the formula,

$m=\frac{y_2-y_1}{x_2-x_1}$

Let us substitute any two coordinates in the formula.

Thus, substituting the coordinates (2,1) and (6,3) in the above formula, we have,

$m=\frac{3-1}{6-2}$

$m=\frac{2}{4}$

$m=\frac{1}{2}$

Thus, the slope of the line is $m=\frac{1}{2}$

Equation of the line:

The equation of the line can be determined using the formula,

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

Let us substitute any one of the coordinates and the slope in the above formula.

Hence, substituting $m=\frac{1}{2}$ and the coordinate (0,0), we get,

$y-0=\frac{1}{2}(x-0)$

     $y=\frac{1}{2}x-0$

     $y=\frac{1}{2}x$

Hence, the equation of the line is $y=\frac{1}{2}x$