Function Analysis: Identifying Y = X + 5 on a Graph

Y is a function of X that matches every value of X where the number is greater by 5.

Which graph describes the function?

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations
00:08 Let's start by drawing the graph of the function.
00:12 Use the function equation given in the problem.
00:16 Substitute X values in, and calculate the matching Y values.
00:21 Then, plot these points on the coordinate grid.
00:27 Remember, always find at least three points to make the graph clear.
00:47 Draw the line that connects your points smoothly.
00:54 And there you have it, the solution to the problem!

Step-by-step written solution

Follow each step carefully to understand the complete solution
1

Understand the problem

Y is a function of X that matches every value of X where the number is greater by 5.

Which graph describes the function?

2

Step-by-step solution

To solve this problem, we will sketch the graph of the function Y=X+5 Y = X + 5 .

  • Step 1: Identify key points by calculating a few points for the graph:
    For X=0 X = 0 , Y=0+5=5 Y = 0 + 5 = 5 .
    For X=1 X = 1 , Y=1+5=6 Y = 1 + 5 = 6 .
    For X=2 X = 2 , Y=2+5=7 Y = 2 + 5 = 7 .
  • Step 2: Plot these points on a Cartesian plane.
    - The points (0,5)(0, 5), (1,6)(1, 6), and (2,7)(2, 7) all lie on the line with a slope of 1.
  • Step 3: Draw the straight line through these points extending in both directions.

As Y=X+5 Y = X + 5 represents a line with a slope of 1 and y-intercept of 5, the line will pass through all these points. Comparing this to the provided graph choices, select the graph with positive slope and y-intercept at 5.

The correct graph is choice 2, which shows a line with a slope of 1 and intercepting the y-axis precisely at 5.

Therefore, the graph that describes the function Y=X+5 Y = X + 5 correctly is choice 2.

3

Final Answer

111222333444555666–1–1–1111222333444555666777888999101010000

Practice Quiz

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Determine whether the following table represents a constant function:

XY02468-3-3-3-3-3

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