Determine the equation of the line to find the relationship between the x- and y-coordinates of points on the line. All lines through the origin are of the form
y=mx, so the equation is
y=x.
A point lies on the line if and only if its y-coordinate is 1/7 of its x-coordinate.
Of the given choices, only choice D,(14,2),satisfies this condition:
2=(14)Choice A is incorrect because the line determined by the origin
(0,0) and
(0,7) is the vertical line with equation x = 0; that is, the y-axis.
The slope of the y-axis is undefined, not
.Therefore,the point(0,7) does not lie on the line that passes the origin and has slope
.
Choices B and C are incorrect because neither of the ordered pairs has a y - coordinate that is
the value of the x - coordinate