Identify the Correct Equation: Linking Values in X: -3 to 1 and Y: 0 to 4

Q: Why can't I just guess which equation fits the table?

Guessing might work sometimes, but calculating the slope systematically ensures you get the right answer every time. Plus, you'll understand why the equation works!

Q: Do I have to use the first two points to find slope?

No! You can use any two points from the table. The slope will be the same regardless of which points you choose, as long as your calculations are correct.

Q: How do I find the y-intercept after getting the slope?

Use the formula $ y = mx + b $ with any point from your table. Substitute the x, y, and slope values, then solve for b.

Q: What if my calculated equation doesn't work for all the points?

This means you made an error! Double-check your slope calculation and y-intercept work. Every point in the table must satisfy your final equation.

Q: Can I use this method for any linear function table?

Absolutely! This slope-intercept method works for all linear functions. Just make sure the points actually form a straight line first.

Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:13 First, let's find the right equation for the function in the table.

00:18 Next, we need to determine the slope of the graph.

00:22 To do this, we’ll use the slope formula.

00:26 Now, we'll plug in the values from the data to find the slope.

00:31 Great! This value is the slope of the graph.

00:36 Let's pick a point on the graph.

00:40 We'll apply the line equation next.

00:45 By substituting the values, we can solve for B.

00:53 This value of B is where the line intersects the Y-axis.

01:00 Finally, let’s put together the line equation using the values we've f ound.

01:06 And there you go! That's how we solve this problem.

Step-by-step written solution

Follow each step carefully to understand the complete solution

1

Understand the problem

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

2

Step-by-step solution

To solve this problem, we will find the linear equation that represents the function in the table by determining the slope and y-intercept.

Step 1: Calculate the slope $m$ .
Between two points $(-3, 0)$ and $-2, 1$ , the slope is:
$m = \frac{1 - 0}{-2 - (-3)} = \frac{1}{1} = 1$
Step 2: Use the slope and a point to find the y-intercept $b$ .
Using the point $(-3, 0)$ and the formula $y = mx + b$ , plug in the values:
$0 = 1(-3) + b$
$0 = -3 + b$
$b = 3$
Step 3: Write the equation of the line:
$y = x + 3$

This linear equation must be consistent with all the points in the table, which it is:

$X = -2$ , $Y = 1$ : $1 + 3 = 4$ , so correct.
$X = -1$ , $Y = 2$ : $2 + 3 = 5$ , so correct.
$X = 0$ , $Y = 3$ : $3$ , so correct.
$X = 1$ , $Y = 4$ : $4 + 3 = 7$ , so correct.

The calculated equation, $y = x + 3$ , matches the option given as Choice 4.

Therefore, the function that corresponds to the table is $y = x + 3$ .

3

Final Answer

$y=x+3$

Key Points to Remember

Essential concepts to master this topic

Slope Formula: Use any two points: $m = \frac{y_2 - y_1}{x_2 - x_1}$
Technique: From (-3,0) to (-2,1): slope = $\frac{1-0}{-2-(-3)} = 1$
Verification: Test all table points in final equation: (-1,2) gives 2 = -1+3 ✓

Common Mistakes

Avoid these frequent errors

Using wrong points or calculating slope incorrectly
Don't mix up coordinates or forget negative signs when calculating $\frac{y_2-y_1}{x_2-x_1}$ = wrong slope and equation! Coordinate errors lead to completely wrong linear functions. Always double-check your coordinate pairs and be extra careful with negative numbers in slope calculations.

Practice Quiz

Test your knowledge with interactive questions

Is the given graph a function?

FAQ

Everything you need to know about this question

Why can't I just guess which equation fits the table?

+

Guessing might work sometimes, but calculating the slope systematically ensures you get the right answer every time. Plus, you'll understand why the equation works!

Do I have to use the first two points to find slope?

+

No! You can use any two points from the table. The slope will be the same regardless of which points you choose, as long as your calculations are correct.

How do I find the y-intercept after getting the slope?

+

Use the formula $y = mx + b$ with any point from your table. Substitute the x, y, and slope values, then solve for b.

What if my calculated equation doesn't work for all the points?

+

This means you made an error! Double-check your slope calculation and y-intercept work. Every point in the table must satisfy your final equation.

Can I use this method for any linear function table?

+

Absolutely! This slope-intercept method works for all linear functions. Just make sure the points actually form a straight line first.

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Identify the Correct Equation: Linking Values in X: -3 to 1 and Y: 0 to 4

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