Identify the Table that Corresponds to the Given Graph: Figure Out the Match!

Q: How do I read coordinates accurately from a graph?

Start with any point on the line. Draw an imaginary vertical line down to the x-axis to find the x-value, then draw an imaginary horizontal line to the y-axis for the y-value. Always double-check by reading at least 3 points!

Q: What if the line doesn't pass exactly through grid intersections?

Look for points where the line does cross grid intersections perfectly. In this problem, the line clearly passes through $ (0,3) $, $ (2,4) $, and $ (4,5) $ exactly.

Q: Do all the points in the table need to match the graph?

Yes, absolutely! Every single coordinate pair in the correct table must correspond to a point that lies on the graphed line. If even one point doesn't match, that table is incorrect.

Q: How can I tell if the relationship is linear?

Check if the rate of change is constant. In this graph, as x increases by 2, y always increases by 1. This consistent pattern $ \frac{\Delta y}{\Delta x} = \frac{1}{2} $ confirms it's linear.

Linear Relationships with Coordinate Tables

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

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Choose the appropriate table

00:03 We want to find points on the graph, and place them in the table

00:07 We'll take a specific X value and find the corresponding Y value according to the graph

00:12 We'll place each point in the table

00:19 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 the following graph, determine which table corresponds to the following table

Step-by-step solution

To solve this problem, we need to determine the table that represents the linear graph shown.

We'll start by analyzing the graph to find specific $X, Y$ points:

The graph passes through the points: $(0, 3), (2, 4),$ and $(4, 5)$ .
This shows that as $X$ increases by 2, $Y$ increases by 1.

Now, let's compare these points with the provided tables:

Choice 1: (1,3), (2,4), (3,5) – Non-matching because first point differs.
Choice 2: (-1,3), (0,4), (1,7) – Non-matching due to different values.
Choice 3: (2,8), (8,3), (10,1) – Non-matching with non-linear change.
Choice 4: (0,3), (2,4), (4,5) – Matches exactly the found graph points.

Therefore, **the table that corresponds to the graph is** $(0,3), (2,4), (4,5)$ . It matches our analysis of the points seen on the graph.

Final Answer

Key Points to Remember

Essential concepts to master this topic

Graph Reading: Identify specific coordinate points from the line
Pattern Recognition: Check if x increases by 2, y increases by 1
Verification: Match all three points (0,3), (2,4), (4,5) with table ✓

Common Mistakes

Avoid these frequent errors

Reading points incorrectly from the graph
Don't estimate coordinates by eye without checking grid lines = wrong table match! This leads to selecting tables with completely different values. Always trace from each point straight down to x-axis and straight left to y-axis to read exact coordinates.

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 read coordinates accurately from a graph?

Start with any point on the line. Draw an imaginary vertical line down to the x-axis to find the x-value, then draw an imaginary horizontal line to the y-axis for the y-value. Always double-check by reading at least 3 points!

What if the line doesn't pass exactly through grid intersections?

Look for points where the line does cross grid intersections perfectly. In this problem, the line clearly passes through $(0,3)$ , $(2,4)$ , and $(4,5)$ exactly.

Do all the points in the table need to match the graph?

Yes, absolutely! Every single coordinate pair in the correct table must correspond to a point that lies on the graphed line. If even one point doesn't match, that table is incorrect.

How can I tell if the relationship is linear?

Check if the rate of change is constant. In this graph, as x increases by 2, y always increases by 1. This consistent pattern $\frac{\Delta y}{\Delta x} = \frac{1}{2}$ confirms it's linear.

What if multiple tables seem to match?

This shouldn't happen if you read coordinates carefully! But if it does, check more points on the line. The correct table will have all points lying exactly on the graphed line.

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