BTGModeratorVI wrote: ↑

Mon Jun 22, 2020 6:13 am

In the rectangular coordinate system, line k is defined by the equation x - 2y + n = 0. What is the value of n?

(1) The x-intercept of line k is 8.
(2) The y-intercept of line k is -4.

Answer: D
Source: Magoosh

KEY CONCEPT: If a point lies ON a line, then the coordinates (x and y) of that point must SATISFY the equation of the line.

Given: Line k is defined by the equation x - 2y + n = 0

Target question: What is the value of n?

Statement 1: The x-intercept of line k is 8
In other words, the point (8, 0) lies ON the line, which means x = 8 and y = 0 SATISFY the equation x - 2y + n = 0
Plug in values to get: 8 - 2(0) + n = 0
Simplify: 8 + n = 0
Solve: n = -8
So, the answer to the target question is n = -8
Since we can answer the target question with certainty, statement 1 is SUFFICIENT

Statement 2: The y-intercept of line k is -4
In other words, the point (0, -4) lies ON the line, which means x = 0 and y = -4 SATISFY the equation x - 2y + n = 0
Plug in values to get: 0 - 2(-4) + n = 0
Simplify: 8 + n = 0
Solve: n = -8
So, the answer to the target question is n = -8
Since we can answer the target question with certainty, statement 2 is SUFFICIENT

Answer: D

Cheers,
Brent