Determine the Corresponding Equation from Tabular Function Data

Q: How do I find the slope from a table?

Pick any two points and use slope = rise/run. For example, from (-2, -4) to (-1, -3): slope = $ \frac{-3-(-4)}{-1-(-2)} = \frac{1}{1} = 1 $

Q: What if the y-intercept isn't directly shown in the table?

Use the point-slope form! Pick any point like (1, -1) and use $ y - (-1) = 1(x - 1) $, then simplify to get $ y = x - 2 $.

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

Check if the change in y-values is constant for equal changes in x-values. In this table, y increases by 1 each time x increases by 1, so it's definitely linear.

Q: Why do I need to check my answer with multiple points?

Testing just one point might work by coincidence! Always verify with at least 2-3 points from the table to make sure your equation is correct.

Q: What if I get confused about which variable is which?

Remember: x is the input, y is the output. In tables, x-values are usually in the top row, y-values in the bottom row. The equation predicts y based on x.

Linear Equations with Tabular Data

Which of the following equations corresponds to the function represented in the table?

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Find the appropriate equation for the function in the table

00:03 We want to find the slope of the graph

00:06 We'll use the formula to find the function graph slope

00:10 We'll substitute appropriate values according to the data and solve to find the slope

00:20 This is the graph's slope

00:27 Let's take a point on the graph

00:32 We'll use the linear equation

00:37 We'll substitute appropriate values and solve for B

00:46 This is the value of B (the Y-axis intercept)

00:49 We'll construct the linear equation using the values we found

00:55 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

Which of the following equations corresponds to the function represented in the table?

Step-by-step solution

To determine the equation corresponding to the values in the table, let's analyze the relationship between X and Y:

Step 1: Check the change in Y with respect to X. The values show that each time X increases by 1, Y increases by 1, indicating a consistent change.
Step 2: Calculate the slope $m$ . Since the change is constant: $\Delta y / \Delta x = 1 / 1 = 1$ . Thus, the slope $m = 1$ .
Step 3: Determine the y-intercept $b$ . When X is 0, Y is -2. Thus, $b = -2$ .
Step 4: Formulate the equation.

y = mx + b

m = 1

b = -2

y = x - 2

Verification with the table: - Substituting $X = -2$ yields $Y = -2 - 2 = -4$ , which matches the table. - Similarly, substituting other values confirms consistency. Hence, this confirms our linear equation.

The corresponding equation for the function represented in the table is therefore $y = x - 2$ .

Final Answer

$y=x-2$

Key Points to Remember

Essential concepts to master this topic

Pattern Recognition: Look for consistent change between consecutive x and y values
Slope Calculation: Use $m = \frac{\Delta y}{\Delta x} = \frac{1}{1} = 1$ for this table
Verification: Substitute each table point into your equation: $y = x - 2$ ✓

Common Mistakes

Avoid these frequent errors

Confusing slope direction or y-intercept sign
Don't assume the y-intercept is positive just because you see negative y-values = wrong equation! Students often write y = x + 2 instead of y = x - 2. Always identify the y-intercept as the y-value when x = 0, which is -2 in this table.

Practice Quiz

Test your knowledge with interactive questions

Determine whether the given graph is a function?

FAQ

Everything you need to know about this question

How do I find the slope from a table?

Pick any two points and use slope = rise/run. For example, from (-2, -4) to (-1, -3): slope = $\frac{-3-(-4)}{-1-(-2)} = \frac{1}{1} = 1$

What if the y-intercept isn't directly shown in the table?

Use the point-slope form! Pick any point like (1, -1) and use $y - (-1) = 1(x - 1)$ , then simplify to get $y = x - 2$ .

How can I tell if the relationship is actually linear?

Check if the change in y-values is constant for equal changes in x-values. In this table, y increases by 1 each time x increases by 1, so it's definitely linear.

Why do I need to check my answer with multiple points?

Testing just one point might work by coincidence! Always verify with at least 2-3 points from the table to make sure your equation is correct.

What if I get confused about which variable is which?

Remember: x is the input, y is the output. In tables, x-values are usually in the top row, y-values in the bottom row. The equation predicts y based on x.

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