Identify the Graph: Function Where Y = X + 3

Q: How do I know which axis the line crosses at 3?

In $ Y = X + 3 $, the +3 is the y-intercept, so the line crosses the y-axis at the point (0, 3). The y-intercept is always where X = 0.

Q: What does slope 1 mean for the graph?

A slope of 1 means the line goes up 1 unit vertically for every 1 unit horizontally. It creates a 45-degree angle going up from left to right.

Q: How can I verify I picked the right graph?

Test a point! Pick any X value, calculate Y using $ Y = X + 3 $, then check if that point lies on your chosen line. For example: when X = 1, Y should be 4.

Q: Why does Y = X + 3 make a straight line?

Any equation in the form $ Y = mX + b $ creates a straight line. The X has no exponents or other operations, so the relationship between X and Y is always constant.

Q: What if I mixed up the slope direction?

Since the slope is positive (+1), the line must go upward from left to right. If you see a line going downward, that's a negative slope and can't be correct.

Linear Functions with Graph Recognition

Since Y is a function of X that matches every value of X where the number is greater by 3

Circle the appropriate graph to describe the function

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Draw the function graph

00:03 Function equation according to the given data

00:08 Substitute values in X and find the corresponding Y values according to the given data

00:12 Plot each point in our coordinate system

00:19 Always find at least 3 points in order to draw a graph

00:49 Draw the appropriate graph

00:52 And this is the solution to the question

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

Since Y is a function of X that matches every value of X where the number is greater by 3

Circle the appropriate graph to describe the function

Step-by-step solution

To solve this problem, we'll follow these steps:

Step 1: Recognize the function $Y = X + 3$ as a linear function.
Step 2: Identify that it has a slope of 1 and a y-intercept at $Y = 3$ .
Step 3: Look for a graph that represents a line with the described characteristics.

Let's apply these steps to solve the problem:
Step 1: The function $Y = X + 3$ suggests a linear relationship.
Step 2: With a slope of 1, the graph rises 1 unit vertically for every 1 unit horizontally. The y-intercept is 3, meaning the line passes through the point $(0, 3)$ .
Step 3: On inspecting the provided choices, identify the graph with the line intersecting the y-axis at 3 and having a slope of 1.

Therefore, the graph that represents the function $Y = X + 3$ is the one given by: choice 1.

Final Answer

Key Points to Remember

Essential concepts to master this topic

Form: Y = X + 3 is linear with slope 1 and y-intercept 3
Method: Find where line crosses y-axis at (0, 3) with upward diagonal
Check: Pick point on line: when X = 1, Y = 4 matches graph ✓

Common Mistakes

Avoid these frequent errors

Confusing slope and y-intercept positions
Don't look for the line crossing at X = 3 instead of Y = 3! This confuses the y-intercept (0, 3) with x-intercept, leading to wrong graph selection. Always remember Y = X + 3 crosses the y-axis at height 3, not the x-axis at position 3.

Practice Quiz

Test your knowledge with interactive questions

Determine whether the following table represents a constant function:

FAQ

Everything you need to know about this question

How do I know which axis the line crosses at 3?

In $Y = X + 3$ , the +3 is the y-intercept, so the line crosses the y-axis at the point (0, 3). The y-intercept is always where X = 0.

What does slope 1 mean for the graph?

A slope of 1 means the line goes up 1 unit vertically for every 1 unit horizontally. It creates a 45-degree angle going up from left to right.

How can I verify I picked the right graph?

Test a point! Pick any X value, calculate Y using $Y = X + 3$ , then check if that point lies on your chosen line. For example: when X = 1, Y should be 4.

Why does Y = X + 3 make a straight line?

Any equation in the form $Y = mX + b$ creates a straight line. The X has no exponents or other operations, so the relationship between X and Y is always constant.

What if I mixed up the slope direction?

Since the slope is positive (+1), the line must go upward from left to right. If you see a line going downward, that's a negative slope and can't be correct.

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