Match the Equation to the Function Table: Identify the Correct Formula

Q: How do I know which two points to use for slope?

You can use any two points from the table! The slope will be the same no matter which pair you choose. Pick points that make calculation easier, like $ (0, 0) $ and $ (3, 1) $.

Q: What if the y-intercept isn't obvious from the table?

Look for the point where x = 0! In this table, when x = 0, y = 0, so the y-intercept is 0. If x = 0 isn't in the table, use $ y = mx + b $ with any point to find b.

Q: Why do I need to check all the points?

Verification ensures accuracy! One correct point doesn't guarantee your equation is right. Check at least 3 points to confirm your equation works for the entire function.

Q: What if my slope comes out negative?

That's totally normal! A negative slope means the function decreases as x increases. Just make sure you calculated $ \frac{y_2 - y_1}{x_2 - x_1} $ correctly with the right order of coordinates.

Q: How is this different from graphing a line?

It's the reverse process! Instead of plotting points from an equation, you're finding the equation from given points. The math concepts are identical - slope and y-intercept.

Linear Functions with Function Tables

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

00:07 We'll use the formula to find the function's graph slope

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

00:20 This is the graph's slope

00:28 Let's take a point on the graph

00:32 We'll use the linear equation

00:35 We'll substitute appropriate values and solve to find B

00:42 This is the value of B

00:46 We'll construct the linear equation using the values we found

00:51 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 solve this problem, let's follow these steps:

Identify key data points given in the problem.
Determine if the data suggests a linear relationship.
Calculate the slope using two points from the table.
Calculate the y-intercept if necessary and match results with possible choices.

First, let's compute the slope $m$ using the first two points: $(-3, -1)$ and $(0, 0)$ . The formula for the slope is:

$m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{0 - (-1)}{0 - (-3)} = \frac{1}{3}$

Next, we can check if any function $y = \frac{1}{3}x + b$ appears in the possible choices. Here since $(0, 0)$ is in the table, this suggests $b = 0$ .

Thus, the equation becomes $y = \frac{1}{3}x$ . This equation corresponds to choice 1. We can verify this by comparing with all given $X, Y$ pairs, and all satisfy the equation $y = \frac{1}{3} x$ .

Therefore, the solution to the problem is $y = \frac{1}{3}x$ .

Final Answer

$y=\frac{1}{3}x$

Key Points to Remember

Essential concepts to master this topic

Function Tables: Show input x-values paired with corresponding output y-values
Slope Calculation: Use $m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{0-(-1)}{0-(-3)} = \frac{1}{3}$
Verification: Check all points satisfy the equation: $\frac{1}{3}(9) = 3$ ✓

Common Mistakes

Avoid these frequent errors

Using wrong points or calculating slope incorrectly
Don't mix up coordinates like using (x₁, y₂) with (x₂, y₁) = wrong slope! This gives you the reciprocal or negative of the correct slope. Always write coordinates clearly: (x₁, y₁) and (x₂, y₂), then substitute carefully into the slope formula.

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 know which two points to use for slope?

You can use any two points from the table! The slope will be the same no matter which pair you choose. Pick points that make calculation easier, like $(0, 0)$ and $(3, 1)$ .

What if the y-intercept isn't obvious from the table?

Look for the point where x = 0! In this table, when x = 0, y = 0, so the y-intercept is 0. If x = 0 isn't in the table, use $y = mx + b$ with any point to find b.

Why do I need to check all the points?

Verification ensures accuracy! One correct point doesn't guarantee your equation is right. Check at least 3 points to confirm your equation works for the entire function.

What if my slope comes out negative?

That's totally normal! A negative slope means the function decreases as x increases. Just make sure you calculated $\frac{y_2 - y_1}{x_2 - x_1}$ correctly with the right order of coordinates.

How is this different from graphing a line?

It's the reverse process! Instead of plotting points from an equation, you're finding the equation from given points. The math concepts are identical - slope and y-intercept.

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