AAPL wrote:Magoosh

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

OA A

The slope of line k is (0 - 9)/(-1 - 2) = -9/-3 = 3. Since (n, 21) is also on the line, the slope between this point and any other point on line k, say (-1, 0), should be 3 also. So we have:

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

21/(n + 1) = 3

7 = n + 1

6 = n

Answer: A

AAPL wrote: ↑

Wed Jun 26, 2019 6:11 am

Magoosh

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

OA A

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

AAPL wrote: ↑

Wed Jun 26, 2019 6:11 am

Magoosh

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

OA A

Solution:

The slope of line k is:

-9/-3 = 3, so we have:

y = 3x + b

We can use (-1,0) to determine the y-intercept:

0 = 3(-1) + b

3 = b

Now we can determine n:

21 = 3n + 3

18 = 3n

6 = n

Alternate Solution:

The slope of line k is:

-9/-3 = 3

We use the slope formula again, using the ordered pairs (-1, 0) and (n, 21):

21/(n + 1) = 3

21 = 3n + 3

18 = 3n

n = 6

Answer: A