IN THE XY-COORDINATE SYSTEM, IF (A+B) ....

[factor26]

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

OA IS D ... can someone please give me a step by step on how to solve this and insight on topic being tested?

Thanks!

[user123321]

slope formed by these two points should be same as slope for the equation given.

slope of those points = (y2-y1)/(x2-x1) = k/3

slope of line is -a/b = -1/-3 = 1/3

equating both slopes => k/3 = 1/3 => k = 1

user123321

[Anurag@Gurome]

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

OA IS D ... can someone please give me a step by step on how to solve this and insight on topic being tested?

Thanks!

Slope of a line passing through 2 points (x1, y1) and (x2, y2) = (y2 - y1)/(x2 - x1)
So, slope of the line passing through (a, b) and (a + 3, b + k) = {(b + k) - b}/{(a + 3) - a} = k/3
Now, slope of the given line x = 3y - 7 (or y = x/3 + 7/3) is 1/3.
Both the slope are equal, so k/3 = 1/3 implies k = 1

The correct answer is D.

[pemdas]

if two points are on the same line, they belong to the function of that line and may be derived by the function of that same line

we are given the slope from the function 3y=x+7, it's 1/3 as y=x/3+7/3

now from the slope formula we set the proportion (b+k-b)/(a+3-a)=1/3 or k/3=1/3 where k=1

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

OA IS D ... can someone please give me a step by step on how to solve this and insight on topic being tested?

Thanks!