Choose the Correct Graph for Y = 3X: Understanding Linear Functions

Q: What does it mean that the line passes through the origin?

Since there's no constant term in $ Y = 3X $, when X = 0, Y = 0. This means the line always passes through point (0,0) on the graph.

Q: Is slope 3 considered steep or gentle?

Slope 3 is quite steep! It's much steeper than slope 1 (45° angle). The line rises quickly as you move from left to right.

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

Pick any point on the line and check: does $ Y = 3X $? For example, if the line goes through (2,6), then 6 = 3(2) ✓. If it goes through (1,4), then 4 ≠ 3(1), so that's wrong!

Q: What if the line doesn't start at (0,0)?

Then it's not the graph of $ Y = 3X $! That would be a different equation like $ Y = 3X + b $ where b ≠ 0. Always check the y-intercept.

Linear Functions with Slope Interpretation

Given that Y is a function of X that matches any value of 3 times X

Choose 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

00:04 The function equation according to the given data

00:06 Substitute values in X and find the corresponding Y values according to the given data

00:20 Plot these points and draw the corresponding graph

00:25 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

Given that Y is a function of X that matches any value of 3 times X

Choose the appropriate graph to describe the function

Step-by-step solution

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

Identify the given function $Y = 3X$ .
Recall that the equation describes a straight line with a slope $m = 3$ and y-intercept $b = 0$ .
Plot the graph as a line through the origin (0,0), rising 3 units for every 1 unit it runs.
Analyze each provided graph to find the graph that matches this description.

Given these steps, start plotting the graph from the origin. The slope of 3 implies a steep line where for each unit moved horizontally (to the right), the line moves three units vertically (upwards).

Examining the graphical choices:

Option 1 correctly represents a line with slope 3 through (0,0).

Therefore, the graph that describes the function $Y = 3X$ is choice Option 1, which matches the linear equation characteristics.

Final Answer

Key Points to Remember

Essential concepts to master this topic

Rule: Y = 3X is a line through origin with slope 3
Technique: For every 1 unit right, move 3 units up (1,3) and (2,6)
Check: Line passes through (0,0) and rises steeply at 3:1 ratio ✓

Common Mistakes

Avoid these frequent errors

Confusing slope direction or steepness
Don't look for a gentle slope when m = 3 = steep upward line! A slope of 3 means the line rises 3 units for every 1 unit horizontally, creating a steep positive line. Always remember that larger slope values create steeper lines.

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 graph shows slope = 3?

Look for a line that goes through the origin (0,0) and rises 3 units up for every 1 unit right. Check points like (1,3) and (2,6) - they should be on the line!

What does it mean that the line passes through the origin?

Since there's no constant term in $Y = 3X$ , when X = 0, Y = 0. This means the line always passes through point (0,0) on the graph.

Is slope 3 considered steep or gentle?

Slope 3 is quite steep! It's much steeper than slope 1 (45° angle). The line rises quickly as you move from left to right.

How can I verify I chose the right graph?

Pick any point on the line and check: does $Y = 3X$ ? For example, if the line goes through (2,6), then 6 = 3(2) ✓. If it goes through (1,4), then 4 ≠ 3(1), so that's wrong!

What if the line doesn't start at (0,0)?

Then it's not the graph of $Y = 3X$ ! That would be a different equation like $Y = 3X + b$ where b ≠ 0. Always check the y-intercept.

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