In the xy-coordinate plane, which of the following points must lie on the line kx + 3y = 6 for every possible value of k

BTGModeratorVI wrote: ↑

Wed Feb 03, 2021 10:32 am

In the xy-coordinate plane, which of the following points must lie on the line kx + 3y = 6 for every possible value of k?

(A) (1,1)
(B) (0,2)
(C) (2,0)
(D) (3,6)
(E) (6,3)

Answer: B
Source: official guide

We're looking for a set of coordinates that are not affected by the value of k.
Notice that, in answer choice B (0,2), the x-coordinate is 0 and y = 2
So, if we plug x = 0 and y = 2 into the equation kx + 3y = 6, we get k(0) + 3(2) = 6
Notice that, since x = 0, the value of k is irrelevant.
So, (0, 2) will ALWAYS be a point on the line kx + 3y = 6

Answer: B

Cheers,
Brent

BTGModeratorVI wrote: ↑

Wed Feb 03, 2021 10:32 am

In the xy-coordinate plane, which of the following points must lie on the line kx + 3y = 6 for every possible value of k?

(A) (1,1)
(B) (0,2)
(C) (2,0)
(D) (3,6)
(E) (6,3)

Answer: B
Source: official guide

Solution:

If a point is on a line with the equation kx + 3y = 6 for every possible value of of k, then x must be 0, since then kx = k(0) = 0. So then we have 3y = 6 or y = 2. Thus the point (0, 2) will always be on the line regardless what the value of k is.

Alternate Solution:

Let’s rewrite the equation kx + 3y = 6 in slope-intercept form y = mx + b:
kx + 3y = 6

3y = -kx + 6

y = -kx/3 + 2

We see that the y-intercept of this line is at 2, and the ordered pair for this y-intercept is (0,2). In other words, when x = 0, then y = 2, and it doesn’t matter what k equals because the term containing k is equal to 0.


Answer: B