In the rectangular coordinate system, if the line \(x = 2y + 5\) passes through points \((m,n)\) and \((m + 2,n + p),\)

[Vincen]

In the rectangular coordinate system, if the line \(x = 2y + 5\) passes through points \((m,n)\) and \((m + 2,n + p),\) what is the value of \(p ?\)

A. -2
B. 0
C. 1/2
D. 1
E. 2

Answer: D

Source: Princeton Review

[Scott@TargetTestPrep]

In the rectangular coordinate system, if the line \(x = 2y + 5\) passes through points \((m,n)\) and \((m + 2,n + p),\) what is the value of \(p ?\)

A. -2
B. 0
C. 1/2
D. 1
E. 2

Answer: D

Solution:

The equation of the given line in slope-intercept form is:

2y + 5 = x

2y = x - 5

y = (1/2)x - 5/2

We see that the given line has a slope of 1/2. We can use the slope formula and substitute the “values” of the points (m,n) and (m + 2, n + p) into it: :

(n + p - n) / (m + 2 - m) = 1/2

p/2 = 1/2

p = 1

Answer: D