Finding the Intersection Point of Two Functions: Graph Analysis Exercise

Q: How do I know which coordinate is x and which is y?

Remember the phrase "x across, y up"! The x-coordinate tells you how far to move horizontally from the origin, and the y-coordinate tells you how far to move vertically.

Q: Do both functions have the same y-value at the intersection?

Yes, absolutely! At the intersection point, both functions must have the same output value. That's exactly what makes it an intersection - both graphs pass through the same point $ (4,2) $.

Q: Why is the intersection point important?

The intersection represents where both functions have equal values. In real-world problems, this might show when two quantities are equal, like when costs are the same or speeds match.

Graph Intersection with Coordinate Reading

At which point does the graph of the first function (I) intersect the graph of the second function (II)?

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Find the intersection point of the graphs

00:03 We'll draw perpendicular lines to each axis, and thus find the values on the axes

00:08 We found that on the X-axis it's 4

00:16 and on the Y-axis it's 2

00:20 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

At which point does the graph of the first function (I) intersect the graph of the second function (II)?

Step-by-step solution

Let's pay attention to the point where the lines intersect. We'll mark it.

We'll find that:

$X=4,Y=2$

Therefore, the point is:

$(4,2)$

Final Answer

$(4,2)$

Key Points to Remember

Essential concepts to master this topic

Intersection: Point where two graphs cross each other on coordinate plane
Reading: Find x-coordinate (4) then y-coordinate (2) at crossing point
Verify: Check that point (4,2) lies on both function graphs ✓

Common Mistakes

Avoid these frequent errors

Reading coordinates in wrong order
Don't read the y-coordinate first as (2,4) instead of (4,2) = wrong intersection point! The x-coordinate always comes first in coordinate pairs. Always read horizontally first (x-value), then vertically (y-value).

Practice Quiz

Test your knowledge with interactive questions

Look at the linear function represented in the diagram.

When is the function positive?

FAQ

Everything you need to know about this question

How do I know which coordinate is x and which is y?

Remember the phrase "x across, y up"! The x-coordinate tells you how far to move horizontally from the origin, and the y-coordinate tells you how far to move vertically.

What if the lines don't seem to cross exactly on a grid point?

Look carefully at the graph! In this problem, the lines cross exactly at x = 4 and y = 2. If it's not on a grid point, you may need to estimate or use the given answer choices.

Do both functions have the same y-value at the intersection?

Yes, absolutely! At the intersection point, both functions must have the same output value. That's exactly what makes it an intersection - both graphs pass through the same point $(4,2)$ .

How can I check if my answer is correct?

Trace each line to the intersection point and verify both coordinates. Function I (blue line) and Function II (red line) both pass through $(4,2)$ , confirming this is the correct intersection point.

Why is the intersection point important?

The intersection represents where both functions have equal values. In real-world problems, this might show when two quantities are equal, like when costs are the same or speeds match.

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