Problem Solving

BTGmoderatorDC wrote:In the xy-coordinate plane, if the point (0,2) lies on the graph of the line 2x + ky = 4, what is the value of the constant k ?

A. 2

B. 1

C. 0

D. -1

E. -2

OA A

Source: Official Guide

KEY CONCEPT: In order for a point to be ON a line, the x- and y-coordinates of the point must satisfy the equation of that line
So, for example, the point (3,7) lies ON the line defined by the equation y = 2x + 1, because x = 3 and y = 7 satisfy the equation y = 2x + 1
That is, 7 = 2(3) + 1

So, if the point (0,2) lies on the graph of the line 2x + ky = 4, then x = 0 and y = 2 must satisfy the equation 2x + ky = 4
Replace x and y with 0 and 2 to get: 2(0) + (k)(2) = 4
Simplify: 0 + 2k = 4
Solve: k = 2

Answer: A

Cheers,
Brent

BTGmoderatorDC wrote:In the xy-coordinate plane, if the point (0,2) lies on the graph of the line 2x + ky = 4, what is the value of the constant k ?

A. 2

B. 1

C. 0

D. -1

E. -2

OA A

Source: Official Guide

We can substitute 0 for x and 2 for y and solve for k:

2(0) + k(2) = 4

2k = 4

k = 2

Answer: A