Graph Intersection: Points on the Line y=2(x+2)-1

Question

Through which points does the function below pass?

y=2(x+2)1 y=2(x+2)-1

Video Solution

Solution Steps

00:00 Find which points are on the line
00:03 Open parentheses properly, multiply by each factor
00:11 This is the equation of the line
00:15 In each point, the left number represents the X-axis and the right represents Y
00:19 Let's substitute each point in the line equation and see if it's possible
00:27 Not possible, therefore the point is not on the line
00:32 We'll use the same method for all points to find which ones are on the line
00:35 Let's move to this point
00:47 Not possible, therefore the point is not on the line
01:06 Possible, therefore the point is on the line
01:12 Let's move to this point
01:21 Not possible, therefore the point is not on the line
01:25 And this is the solution to the question

Step-by-Step Solution

To determine through which points the function y=2(x+2)1 y = 2(x+2) - 1 passes, let's proceed methodically.

Step 1: Simplify the expression of the linear function:

The given function is y=2(x+2)1 y = 2(x+2) - 1 . Distribute the 2 2 over the terms inside the parenthesis:
y=2x+41 y = 2x + 4 - 1

Simplify further by combining like terms:
y=2x+3 y = 2x + 3

Step 2: Evaluate the function at different x x -values to find which points lie on the line represented by the function y=2x+3 y = 2x + 3 .

Step 3: Check each of the provided choice points:

  • For choice (0,0) (0,0) : Substituting x=0 x = 0 into y=2x+3 y = 2x + 3 , we get y=2(0)+3=3 y = 2(0) + 3 = 3 . This does not match y=0 y = 0 .
  • For choice (10,13) (10,13) : Substituting x=10 x = 10 into y=2x+3 y = 2x + 3 , we get y=2(10)+3=23 y = 2(10) + 3 = 23 . This does not match y=13 y = 13 .
  • For choice (5,13) (5,13) : Substituting x=5 x = 5 into y=2x+3 y = 2x + 3 , we get y=2(5)+3=13 y = 2(5) + 3 = 13 . This matches y=13 y = 13 , so this point lies on the line.
  • For choice (4,13) (4,13) : Substituting x=4 x = 4 into y=2x+3 y = 2x + 3 , we get y=2(4)+3=11 y = 2(4) + 3 = 11 . This does not match y=13 y = 13 .

Therefore, the point through which the given function passes is (5,13) (5,13) .

Answer

(5,13) (5,13)