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

Q: How do I find the y-intercept quickly?

Set X = 0 in your equation! For $ Y = X + 5 $, when X = 0: Y = 0 + 5 = 5. So the y-intercept is 5, meaning the line crosses the y-axis at point (0, 5).

Q: What does 'greater by 5' mean in the problem?

It means Y is always 5 more than X. If X = 2, then Y = 2 + 5 = 7. This translates directly to the equation $ Y = X + 5 $.

Q: How can I tell if a line has slope 1?

A slope of 1 means the line goes up 1 unit vertically for every 1 unit horizontally. It makes a 45° angle and looks like it's climbing stairs with equal steps.

Q: Which graph should I choose?

Look for a line that crosses the y-axis at 5 and has a positive slope. The line should go up from left to right, passing through points like (0, 5), (1, 6), and (2, 7).

Q: Can I check my answer using other points?

Yes! Pick any X value and calculate Y. For example: if X = 3, then Y = 3 + 5 = 8. The point (3, 8) should be on your chosen line.

Linear Functions with Y-Intercept Identification

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

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?

Step-by-step solution

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

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

As $Y = X + 5$ 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 $Y = X + 5$ correctly is choice 2.

Final Answer

Key Points to Remember

Essential concepts to master this topic

Function Form: Y = X + 5 is linear with slope 1 and y-intercept 5
Key Points: When X = 0, Y = 5; when X = 1, Y = 6
Verification: Check that the line passes through (0,5) and has positive slope ✓

Common Mistakes

Avoid these frequent errors

Confusing the y-intercept with the x-intercept
Don't look for where the line crosses the x-axis at Y = 5! This gives completely wrong graph selection. The y-intercept occurs when X = 0, so Y = 0 + 5 = 5. Always identify where the line crosses the y-axis at the point (0, 5).

Practice Quiz

Test your knowledge with interactive questions

Determine whether the given graph is a function?

FAQ

Everything you need to know about this question

How do I find the y-intercept quickly?

Set X = 0 in your equation! For $Y = X + 5$ , when X = 0: Y = 0 + 5 = 5. So the y-intercept is 5, meaning the line crosses the y-axis at point (0, 5).

What does 'greater by 5' mean in the problem?

It means Y is always 5 more than X. If X = 2, then Y = 2 + 5 = 7. This translates directly to the equation $Y = X + 5$ .

How can I tell if a line has slope 1?

A slope of 1 means the line goes up 1 unit vertically for every 1 unit horizontally. It makes a 45° angle and looks like it's climbing stairs with equal steps.

Which graph should I choose?

Look for a line that crosses the y-axis at 5 and has a positive slope. The line should go up from left to right, passing through points like (0, 5), (1, 6), and (2, 7).

Can I check my answer using other points?

Yes! Pick any X value and calculate Y. For example: if X = 3, then Y = 3 + 5 = 8. The point (3, 8) should be on your chosen line.

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