In the xy-coordinate system, if (m, n) and (m 1 2, n 1 k) are two points on the line
with the equation x 5 2y 1 5, then k 5	Select the correct option:
A) 1 / 2
B) 1
C) 2
D) 5 / 2
E) 4

Rationale: step 1 : analyze the question for any question involving the equation of a line , a good place to start is the slope - intercept form of the line , y = mx 1 b . remember that if you have two points on a line , you can derive the entire equation , and if you have an equation of the line , you can calculate any points on that line . step 2 : state the task we are solving for k , which is the amount by which the y - coordinate increases when the x - coordinate increases by 2 . step 3 : approach strategically the slope of a line is the ratio between the change in y and the change in x . in other words , every time the x - coordinate increases by 1 , the y - coordinate increases by the amount of the slope . the equation of the line in the question stem is defined as x = 2 y + 5 . we must isolate y to have slope - intercept form : so the slope of this line is 1 / 2 . this means that for every change of + 1 in the x direction , there is a change of + 1 / 2 in the y direction . then we know that , because there is an increase in 2 units in the x direction when moving from m to m + 2 , there must be a change of 1 unit in the y direction when moving from n to n + k . so k = 1 . since there are variables that eventually cancel ( m and n are not part of the answers ) , we can pick numbers . let ’ s say that you choose the y - coordinate of the point ( m , n ) to be 0 to allow for easier calculations . using the equation we ’ re given to relate x - and y - coordinates , we can calculate the x - coordinate : so ( m , n ) is the point ( 5 , 0 ) . now we ’ ll plug our values of m and n into the next point : ( m + 2 , n + k ) . that yields ( 7 , k ) . all we have to do is plug an x - coordinate of 7 into the equation to solve for k , the y - coordinate : answer is b
Answer: B