Problem Solving

BTGModeratorVI wrote: ↑

Sat Aug 08, 2020 7:02 am

In the xy-coordinate system, points (2, 9) and (-1, 0) lie on line k. If the point (n, 21) lies on line k, what is the value of n?

A. 6
B. 7
C. 8
D. 9
E. 10

Answer: A
Source: Magoosh

Key concept: If you take any portion of a particular line, the slope between ANY two points on the line will always be the same.

So, for example, the slope between points (2, 9) and (-1, 0) must be equal to the slope between points (2, 9) and (n, 21)

Slope between (2, 9) and (-1, 0) = (9 - 0)/(2 - (-1)) = 9/3 = 3

This means the slope between points (2, 9) and (n, 21) must also equal 3

We can write: (21 - 9)/(n - 2) = 3
Simplify: 12/(n - 2) = 3
Multiply both sides by (n - 2) to get: 12 = 3(n - 2)
Divide both sides by 3 to get: 4 = n - 2
Solve: n = 6

Answer: A

Cheers,
Brent

BTGModeratorVI wrote: ↑

Sat Aug 08, 2020 7:02 am

In the xy-coordinate system, points (2, 9) and (-1, 0) lie on line k. If the point (n, 21) lies on line k, what is the value of n?

A. 6
B. 7
C. 8
D. 9
E. 10

Answer: A

Solution:

The slope of line k is:

(9 - 0) / (2 - (-1)) = 9/3 = 3

Therefore, if (n, 21) lies on line k, it must have a slope of 3 with any of the two given points. Let’s use the latter and create the equation:

(21 - 0) / (n - (-1)) = 3

21 / (n + 1) = 3

21 = 3n + 3

18 = 3n

6 = n

Answer: A