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...

BTGmoderatorLU wrote: ↑

Wed Sep 30, 2020 10:01 am

Source: Official Guide

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

The OA is D

Solution:

Recall that an ordered pair represents a pair of x and y coordinates. Substituting the values from the first ordered pair (a,b) into the equation, we can create the following equation:

a = 3b - 7

Substituting the values from the second ordered pair for x and y into the same equation, we have:

a + 3 = 3(b + k) - 7 → a + 3 = 3b + 3k - 7

If we subtract the first equation from the second, we have:

3 = 3k

1 = k

Answer: D

BTGmoderatorLU wrote: ↑

Wed Sep 30, 2020 10:01 am

Source: Official Guide

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

The OA is D

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 = 3y - 7
One point ON the line is (a, b)
So, we can write: a = 3b - 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