Graph to Table Analysis: Determine the Matching Dataset

Linear Functions with Coordinate Analysis

Given the following graph, determine which table corresponds to the following table

–6–6–6–5–5–5–4–4–4–3–3–3–2–2–2–1–1–1111222333444555666777888999–1–1–1111222333444555666777000

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations
00:00 Choose the appropriate table for the graph
00:03 We want to find points on the graph, and place them in the table
00:06 We'll take a specific X value and find the corresponding Y value according to the graph
00:14 We'll place each point in the table
00:21 And this is the solution to the question

Step-by-step written solution

Follow each step carefully to understand the complete solution
1

Understand the problem

Given the following graph, determine which table corresponds to the following table

–6–6–6–5–5–5–4–4–4–3–3–3–2–2–2–1–1–1111222333444555666777888999–1–1–1111222333444555666777000

2

Step-by-step solution

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

  • Identify key points on the graph where lines cross grid intersections.
  • Convert these intersections into coordinate pairs (X, Y).
  • Compare these pairs with each table of choices provided.

Now, let's work through each step:
Find two key points on the graph that you can identify where the line crosses grid intersections. From the graph, we can see:

  • Point 1: (0,0) (0, 0)
  • Point 2: (1,5) (1, 5)
  • Point 3: (2,6) (2, 6)

These points indicate the graph’s relationship in the form of a linear equation.

Let's compare these points to the tables:
Choice 1 has the following data points:

  • (0,1)(0, 1)
  • (1,2)(1, 2)
  • (2,3)(2, 3)

This does not match.

Choice 2 has these data points:

  • (0,1)(0, -1)
  • (1,2)(1, -2)
  • (2,3)(2, -3)

This does not match either.

Choice 3 has these data points:

  • (0,0)(0, 0)
  • (1,5)(1, 5)
  • (2,6)(2, 6)

This set of points matches perfectly.

Therefore, the solution to the problem is Choice 3.

3

Final Answer

XY012056

Key Points to Remember

Essential concepts to master this topic
  • Point Identification: Find precise coordinates where the line crosses grid intersections
  • Pattern Recognition: Extract points like (0,0), (1,5), (2,6) from the graph
  • Verification: Match all identified points with corresponding table values ✓

Common Mistakes

Avoid these frequent errors
  • Reading approximate points instead of exact grid intersections
    Don't guess at coordinates from visual estimation = wrong table match! Approximating leads to selecting incorrect data tables. Always identify points where the line passes exactly through grid line intersections.

Practice Quiz

Test your knowledge with interactive questions

Determine whether the given graph is a function?

–7–7–7–6–6–6–5–5–5–4–4–4–3–3–3–2–2–2–1–1–1111222333444555666777–4–4–4–3–3–3–2–2–2–1–1–1111222333000

FAQ

Everything you need to know about this question

How do I know which points on the line to use?

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Look for points where the line crosses exactly at grid intersections. These give you precise coordinates like (0,0) (0, 0) , (1,5) (1, 5) , and (2,6) (2, 6) .

What if the line doesn't pass through clear grid points?

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In this problem, the line does pass through clear intersections. If it didn't, you'd need to estimate carefully or use the equation of the line to calculate exact values.

Why can't I just pick any points on the line?

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You can use any points, but grid intersections are easiest to read accurately. Using unclear points leads to measurement errors and wrong table selection.

How do I check if my chosen table is correct?

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Verify that every coordinate pair from your graph matches the table exactly. If even one point doesn't match, that table is incorrect.

What does the slope of this line tell me?

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The line goes from (0,0) (0, 0) to (1,5) (1, 5) , so the slope is 5. This steep positive slope helps confirm the correct table shows large y-value increases.

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