Graph Analysis: Mapping Graph Points to Corresponding Data Table

Q: How do I know which points to pick from the graph?

Choose points where the line clearly crosses grid intersections. Avoid points between grid lines where you have to estimate. Points like (1,1) and (2,2) are perfect because they're exact!

Q: Do I need to check all the x-values in each table?

Yes! A table is only correct if every single point satisfies your equation. If even one point fails, that table is wrong. For $ Y = X $, check that each x equals its corresponding y.

Q: What if two tables seem to work?

This shouldn't happen if you have the correct equation! Recheck your slope calculation and make sure you're testing all points in each table, not just one or two.

Linear Relationships with Coordinate Point Analysis

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

00:04 Find points on the graph to determine the graph equation

00:21 This is the function equation

00:25 We will deduce the appropriate table from the equation

00:29 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'll follow these steps:

Step 1: Identify two points from the graph to determine the line's equation.
Step 2: Calculate the slope $m$ .
Step 3: Use the slope to find the y-intercept $c$ .
Step 4: Write the equation of the line $Y = mX + c$ .
Step 5: Check each given table to see which one matches the line's equation.

Let's proceed with these steps:
Step 1: Looking at the graph, we pick two points, let's say $(1, 1)$ and $(2, 2)$ .
Step 2: Calculate the slope: $m = \frac{2 - 1}{2 - 1} = 1$ .
Step 3: Use one of the points $(1, 1)$ to find the y-intercept: since $Y = mX + c$ , $1 = 1(1) + c$ , hence $c = 0$ .
Step 4: The line's equation is therefore $Y = X$ .
Step 5: Examine the tables:

Choice 1: $X: -1, 0, 1$ and $Y: -1, 0, 1$ matches our line $Y = X$ .
Other choices fail this test because they do not satisfy the equation.

Therefore, the correct table that corresponds to the graph is choice 1.

Final Answer

Key Points to Remember

Essential concepts to master this topic

Graph Reading: Identify at least two clear points from the line
Slope Formula: Calculate $m = \frac{y_2 - y_1}{x_2 - x_1}$ using points (1,1) and (2,2)
Table Verification: Check each x-value produces correct y-value using $Y = X$ ✓

Common Mistakes

Avoid these frequent errors

Reading graph points incorrectly or choosing unclear points
Don't estimate points from blurry grid intersections = wrong slope calculation! Unclear points lead to incorrect equations that don't match any table. Always choose points where the line clearly passes through grid intersections like (1,1) and (2,2).

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 points to pick from the graph?

Choose points where the line clearly crosses grid intersections. Avoid points between grid lines where you have to estimate. Points like (1,1) and (2,2) are perfect because they're exact!

What if I get a different slope than 1?

Double-check your chosen points! If the line goes through (0,0), (1,1), and (2,2), the slope must be 1. Reread the graph carefully and pick clearer intersection points.

Do I need to check all the x-values in each table?

Yes! A table is only correct if every single point satisfies your equation. If even one point fails, that table is wrong. For $Y = X$ , check that each x equals its corresponding y.

What if two tables seem to work?

This shouldn't happen if you have the correct equation! Recheck your slope calculation and make sure you're testing all points in each table, not just one or two.

Can I use the y-intercept to help identify the correct table?

Absolutely! The y-intercept is where the line crosses the y-axis. In this graph, when x = 0, y = 0, so the y-intercept is 0. This confirms our equation $Y = X$ .

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