Representations of Functions: Matching a graph to a table

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.

To solve this problem, observe that the graph represents a horizontal line at some constant $y$-value.

We need to identify which table reflects this characteristic, meaning the $y$-values must all be the same for listed $x$-values. Let's evaluate the choices:

• Choice 1: $y$-values are 2, 3, 4 for $x = -1, 0, 1$. This is not constant.
• Choice 2: $y$-values are 4, 4, 4 for $x = -1, 0, 1$. This represents a constant function where $y$ is always 4.
• Choice 3: $y$-values are 5, 8, 11 for $x = -1, 0, 1$. This is not constant.
• Choice 4: $y$-values are 3, 8, 13 for $x = -1, 0, 1$. This is not constant.

The choice that matches the graph, depicting a horizontal line at a consistent $y$-value, is Choice 2. Therefore, the table corresponding to the graph is:

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

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:

• $(0, 1)$
• $(1, 2)$
• $(2, 3)$

This does not match.

Choice 2 has these data points:

• $(0, -1)$
• $(1, -2)$
• $(2, -3)$

This does not match either.

Choice 3 has these data points:

• $(0, 0)$
• $(1, 5)$
• $(2, 6)$

This set of points matches perfectly.

Therefore, the solution to the problem is Choice 3.

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

• Step 1: Identify key points on the graph.

• Step 2: Cross-reference these points with each option table.

Let's work through each step:
Step 1: The graph appears to pass through points $(0, 0)$, $(1, 2)$, and $(2, 1)$.
Step 2: Reviewing each table:

• Choice 1: Points $(0, 0)$, $(1, 2)$, and $(2, 1)$ exactly match the data in this table.

• Choice 2: This table does not match the sequence $(0, 0)$, $(1, 2)$, $(2, 1)$ directly.

• Choice 3: The ordering or values do not match with $(0, 0)$, $(1, 2)$, $(2, 1)$.

• Choice 4: The values are swapped and thus do not match the identified points.

Thus, the table in Choice 1 matches the graph, with the points $(0, 0)$, $(1, 2)$, and $(2, 1)$, aligning perfectly with the graph's intersections.

Therefore, the solution is the table under Choice 1.

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

• Step 1: Analyze the graph to identify clear points of intersection with integer coordinates.

• Step 2: Compare these identified points with each table option to find the correct match.

Now, let's work through each step:
Step 1: Upon inspecting the graph, observe the plotted points of intersection:
- When $X = 2$, $Y = 3$ - When $X = 3$, $Y = 2$ - When $X = 4$, $Y = 1$
Step 2: Next, compare these coordinates with each choice provided:

• - Option 1: Coordinates do not match.

• - Option 2: Coordinates do not match.

• - Option 3: Matches $(2, 3)$, $(3, 2)$, $(4, 1)$.

• - Option 4: Coordinates do not match.

Therefore, the solution to the problem is Choice 3.

We carefully identified points on the graph and matched them to the provided tables to select the correct option.

To determine which table corresponds to the given graph, we'll follow these steps:

• Extract coordinates from the graph that clearly intersect grid lines for precision.

• Compare these extracted coordinates with the provided tables to find a match.

• Ensure consistency across multiple points.

Let's extract some sample points from the graph:
- Observing the graph visually, we can see the following intersection points: (0, 6), (3, 3), and (6, 0). These clearly depict the trend visible in the linear graph.

We will compare these extracted points to the tables:

• Choice 1: Points are (-5, 0), (-4, 1), (-3, 2). This does not match our points.

• Choice 2: Points are (8, 10), (6, 6), (4, 2). This does not match our points.

• Choice 3: Points are (0, 6), (3, 3), (6, 0). This matches exactly with the points from the graph.

• Choice 4: Points are (0, 0), (2, 3), (4, 2). This does not match our points.

Therefore, the table that matches the graph is the one in Choice 3.

As a result, the solution is that the correct table is from choice 3, which includes the points (0, 6), (3, 3), and (6, 0).

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.

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

• Step 1: Identify points on the graph.
• Step 2: Compare these points with those given in the tables.
• Step 3: Determine which table matches these points.

Now, let's work through each step:
Step 1: Upon inspecting the graph, we identify the points: $(-2, 4)$, $(0, 4)$, $(2, 2)$, and $(4, 0)$.
Step 2: We compare these points with the sets of points in each table choice.
Step 3: After comparing, we find that the table with $(X, Y)$ values $(0, 4)$, $(2, 2)$, and $(4, 0)$ matches the points from the graph.

Therefore, the correct table that corresponds to the given graph is Choice 2.

To find the table corresponding to the graph, let's proceed step-by-step:

• Step 1: Identify points from the graph.
• Step 2: Deduce the coordinates by examining the graph.
• Step 3: Compare these coordinates to those listed in the choices.

Step 1: Observing the graph, it passes through the following points: $(-3,1)$, $(0,1)$, and $(3,0)$.

Step 2: We deduce these points by checking intersections where the line crosses a visible grid point.

Step 3: Now, compare these points to the tables given in the options:

• Choice 1: Matches $(-3,1)$, $(0,1)$, $(3,0)$.
• Choice 2, 3, and 4: Do not match these points based on given coordinates.

Therefore, the table that matches the graph's data points is Choice 1.

The correct table according to the graph is: $\begin{array}{|c|c|c|}\hline X & -3 & 0 & 3 \\ \hline Y & 1 & 1 & 0 \\ \hline \end{array}$

To solve this problem, we will follow these steps:

• Step 1: Examine the graph and identify the points that stand out on the graph.
• Step 2: Analyze the coordinates of these points by looking at the $X$ and $Y$ axes.
• Step 3: Compare these coordinates to the provided table choices.

Now, let's go through each step in detail:

Step 1: Upon examining the graph, it depicts a piecewise linear graph passing through several key points. Notably, there's a horizontal segment and a slanted segment forming a "V" shape. Consider the points where the line changes direction or intersects with an axis.

Step 2: Looking closely, we can identify three main points from the graph: - At $x = -4$, $y = -1$. - At $x = 0$, $y = -1$. - At $x = 4$, $y = 3$.

Step 3: Next, we compare these coordinates to the options provided as tables:

1. Choice 1 suggests points $(x,y): (1,3), (2,4), (3,5)$ which does not match our graph.
2. Choice 2 has $(x,y): (-1,3), (0,4), (1,7)$ which also does not fit the described graph.
3. Choice 3 presents $(x,y): (-4,-1), (0,-1), (4,3)$ which exactly matches all the observed points from our examination of the graph!
4. Choice 4 offers $(x,y): (0,3), (2,4), (4,5)$ which again is not comparable with the graph.

Thus, upon reviewing all the choices, we determine that the correct table corresponding to the graph is Choice 3.

Therefore, the solution to the problem is Choice 3.