The equation of the line is [tex]y=\frac{1}{2}x[/tex]
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,
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]
Let us substitute any two coordinates in the formula.
Thus, substituting the coordinates (2,1) and (6,3) in the above formula, we have,
[tex]m=\frac{3-1}{6-2}[/tex]
[tex]m=\frac{2}{4}[/tex]
[tex]m=\frac{1}{2}[/tex]
Thus, the slope of the line is [tex]m=\frac{1}{2}[/tex]
Equation of the line:
The equation of the line can be determined using the formula,
[tex]y-y_1=m(x-x_1)[/tex]
Let us substitute any one of the coordinates and the slope in the above formula.
Hence, substituting [tex]m=\frac{1}{2}[/tex] and the coordinate (0,0), we get,
[tex]y-0=\frac{1}{2}(x-0)[/tex]
[tex]y=\frac{1}{2}x-0[/tex]
[tex]y=\frac{1}{2}x[/tex]
Hence, the equation of the line is [tex]y=\frac{1}{2}x[/tex]
