Carcass wrote:

In the xy-coordinate system, if (a,b) and (a+3, b+k) are two points on the line defined by the equation x=3y-7, then k=?

A. 9

B. 3

C. 7/3

D. 1

E. 1/3

Kudos for the right answer and explanation

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

x = 3

y - 7

One point ON the line is (

a,

b)

So, we can write:

a = 3

b - 7

Another point ON the line is (

a + 3,

b + k)

So, we can write:

a + 3 = 3(

b + k) - 7

Expand: a + 3 = 3b + 3k - 7

Subtract 3 from both sides to get: a = 3b + 3k - 10

We now two equations:

a = 3b + 3k - 10

a = 3b - 7

Subtract the bottom equation from the top equation to get: 0 = 3k - 3

Add 3 to both sides: 3 = 3k

Solve: k = 1

Answer: D

Cheers,

Brent

_________________

Brent Hanneson – Creator of greenlighttestprep.com

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