Linear Function: Find the Equation from Table Values (2,13) to (-1,4)

Q: Which two points should I pick from the table?

You can use any two points from the table! For this problem, (2,13) and (-1,4) work great, or you could use (1,10) and (0,7). The slope will always be the same.

Q: Why is the y-intercept 7 when x = 0?

The y-intercept is where the line crosses the y-axis, which happens when x = 0. Looking at the table, when x = 0, y = 7, so the y-intercept is 7.

Q: What if my slope comes out negative?

A negative slope means the line goes down from left to right. Always double-check your subtraction: $ \frac{y_2 - y_1}{x_2 - x_1} $ - order matters!

Q: Can I solve this without finding the y-intercept separately?

Yes! Use the point-slope form: $ y - y_1 = m(x - x_1) $. With slope 3 and point (2,13): $ y - 13 = 3(x - 2) $, then simplify to get $ y = 3x + 7 $.

Q: How can I check my final equation?

Substitute each table point into your equation! For $ y = 3x + 7 $: when x = 2, $ y = 3(2) + 7 = 13 $ ✓. Try all points to be sure!

Linear Equations with Table Analysis

Below is a table containing values for x and y. This tables represents a linear function.

Choose the equation that corresponds to the function.

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Find the algebraic representation of the given table

00:04 Take 2 given points

00:12 Use the formula to find slope using 2 points on graph

00:18 Substitute appropriate values according to the data and solve to find the slope

00:30 This is the slope of the graph

00:38 Use the formula for linear function representation

00:44 Substitute the points and solve to find the unknown B

00:55 This is the intersection point with Y-axis (the unknown B)

01:03 Appropriately substitute the slope and intersection point to find the function

01:11 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

Below is a table containing values for x and y. This tables represents a linear function.

Choose the equation that corresponds to the function.

Step-by-step solution

To determine the equation of the linear function from the given table, we'll follow these steps:

Step 1: Calculate the Slope ( $m$ )
Step 2: Find the Y-intercept ( $b$ )
Step 3: Formulate the Linear Equation

Let's delve into each step:

Step 1: Calculate the Slope ( $m$ )
Using two points from the table, $(2, 13)$ and $(1, 10)$ , we calculate the slope $m$ using the formula:

$m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{10 - 13}{1 - 2} = \frac{-3}{-1} = 3$

Thus, the slope $m$ is 3.

Step 2: Find the Y-intercept ( $b$ )
The y-intercept $b$ is easily found because it is where $x = 0$ . From the table, when $x = 0$ , $y = 7$ , therefore $b = 7$ .

Step 3: Formulate the Linear Equation
Substitute the values of $m$ and $b$ into the linear equation format:

$y = 3x + 7$

Hence, the equation that represents the linear function is $y = 3x + 7$ .

Checking against the provided choices, the equation corresponds to choice 2.

Final Answer

$y=3x+7$

Key Points to Remember

Essential concepts to master this topic

Slope Formula: Use $m = \frac{y_2 - y_1}{x_2 - x_1}$ with any two points
Y-intercept Method: Find where x = 0, or use $y = mx + b$ with known point
Verification: Check equation works for all table points: (2,13), (1,10), (0,7), (-1,4) ✓

Common Mistakes

Avoid these frequent errors

Using wrong points or calculating slope incorrectly
Don't mix up x and y coordinates when calculating slope = wrong equation! Students often write $\frac{x_2 - x_1}{y_2 - y_1}$ instead of $\frac{y_2 - y_1}{x_2 - x_1}$ , or use points incorrectly. Always write coordinates clearly as (x,y) and follow the slope formula exactly.

Practice Quiz

Test your knowledge with interactive questions

For the function in front of you, the slope is?

FAQ

Everything you need to know about this question

Which two points should I pick from the table?

You can use any two points from the table! For this problem, (2,13) and (-1,4) work great, or you could use (1,10) and (0,7). The slope will always be the same.

Why is the y-intercept 7 when x = 0?

The y-intercept is where the line crosses the y-axis, which happens when x = 0. Looking at the table, when x = 0, y = 7, so the y-intercept is 7.

How do I know if I calculated the slope correctly?

Check your slope by using it with different points! If slope = 3, then from (0,7) to (1,10): $\frac{10-7}{1-0} = \frac{3}{1} = 3$ ✓

What if my slope comes out negative?

A negative slope means the line goes down from left to right. Always double-check your subtraction: $\frac{y_2 - y_1}{x_2 - x_1}$ - order matters!

Can I solve this without finding the y-intercept separately?

Yes! Use the point-slope form: $y - y_1 = m(x - x_1)$ . With slope 3 and point (2,13): $y - 13 = 3(x - 2)$ , then simplify to get $y = 3x + 7$ .

How can I check my final equation?

Substitute each table point into your equation! For $y = 3x + 7$ : when x = 2, $y = 3(2) + 7 = 13$ ✓. Try all points to be sure!

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