Through Which Points Does the Graph of x = y - 4 + 2x Pass?

Question

Look at the following function:

x=y4+2x x=y-4+2x

Through which of the following points does the graph of the function pass?

Video Solution

Solution Steps

00:00 Find through which points the function passes
00:03 Let's arrange the function, isolate Y
00:16 This is the function equation
00:19 In each point, the left number represents X-axis and the right Y
00:23 Let's substitute each point in the line equation and see if possible
00:31 Possible, therefore the point is on the line
00:34 Let's use the same method and find which points are on the line
00:37 Moving to the second point, let's substitute in the line equation
00:42 Not possible, therefore the point is not on the line
00:45 Moving to the third point, let's substitute in the line equation
00:51 Not possible, therefore the point is not on the line
00:54 Moving to the fourth point, let's substitute in the line equation
01:05 Not possible, therefore the point is not on the line
01:08 And this is the solution to the question

Step-by-Step Solution

To determine through which point the function passes, we begin by simplifying the given equation.

Given: x=y4+2x x = y - 4 + 2x

Rearranging the terms to solve for y y :

x=y4+2x x = y - 4 + 2x

Subtract x x from both sides to isolate the terms involving y y :

0=y4+x 0 = y - 4 + x

Rearrange to solve for y y :

y=x+4 y = -x + 4

Now, we will test each point to see which satisfies the equation y=x+4 y = -x + 4 .

  • For (1,5) (-1, 5) , substitute x=1 x = -1 :
  • y=(1)+4=1+4=5 y = -(-1) + 4 = 1 + 4 = 5

    This point satisfies the equation.

  • For (0,5) (0, 5) , substitute x=0 x = 0 :
  • y=(0)+4=4 y = -(0) + 4 = 4

    This point does not satisfy the equation.

  • For (1,5) (1, 5) , substitute x=1 x = 1 :
  • y=(1)+4=1+4=3 y = -(1) + 4 = -1 + 4 = 3

    This point does not satisfy the equation.

  • For (2,5) (2, 5) , substitute x=2 x = 2 :
  • y=(2)+4=2+4=2 y = -(2) + 4 = -2 + 4 = 2

    This point does not satisfy the equation.

Therefore, the graph of the function passes through the point (1,5)(-1, 5).

Answer

(1,5) (-1,5)