GMATinsight wrote:
A line in the xy-plane passes through the origin and has a slope of 1/7 Which of the following points lies on the line?
A) (0, 7)
B) (1, 7)
C) (7, 7)
D) (14, 2)
E) (7, 14)
Let's write the equation of the line in
slope y-intercept form y = mx + b, where m = the slope and b = the y-intercept.
So, m = 1/7
And, since the line passes through the origin (0,0), we know that b (the y-intercept) = 0
So, the equation of the line is: y = (1/7)x + 0
Or just y = (1/7)x
So, all points (x, y) ON the line will satisfy the equation y = (1/7)x
Let's check the answer choices.
A) (0, 7) plug x = 0 and y = 7 into the equation of the line to get: 7 = (1/7)(0) Doesn't work. So, (0,7) is NOT on the line.
B) (1, 7) plug x = 1 and y = 7 into the equation of the line to get: 7 = (1/7)(1) Doesn't work. So, (1,7) is NOT on the line.
C) (7, 7) plug x = 7 and y = 7 into the equation of the line to get: 7 = (1/7)(7) Doesn't work. So, (7,7) is NOT on the line.
D) (14, 2) plug x = 14 and y = 2 into the equation of the line to get: 2 = (1/7)(14) This WORKS. So, (2,14) IS on the line.
Answer: D