Find the Passing Points: y = 6(2x + 4) + x

Q: Do I have to distribute first, or can I substitute x = 0 right away?

You can substitute directly, but distributing first shows the simplified form $ y = 13x + 24 $. This makes it easier to find other points and understand the function's behavior.

Q: How do I know which terms to combine?

Look for like terms - terms with the same variable and exponent. Here, 12x and x are like terms, so 12x + x = 13x. The constant 24 stands alone.

Q: What if I need to find where the function passes through other points?

Once you have $ y = 13x + 24 $, substitute any x-value you want! For example: when x = 1, y = 13(1) + 24 = 37, so it passes through (1, 37).

Q: Can I check my answer using a different x-value?

Absolutely! Try x = 1: Original equation gives $ y = 6(2(1) + 4) + 1 = 6(6) + 1 = 37 $. Simplified form gives $ y = 13(1) + 24 = 37 $ ✓

Linear Functions with Distributive Property

Through which points does the function below pass?

$y=6(2x+4)+x$

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Find which points are on the line

00:03 Open parentheses properly, multiply by each factor

00:14 This is the line equation

00:17 In each point, the left number represents the X-axis and the right represents Y

00:21 We'll substitute each point in the line equation and see if it's possible

00:28 Not possible, therefore the point is not on the line

00:31 We'll use the same method for all points and find which ones are on the line

00:34 Let's move to this point

00:43 Not possible, therefore the point is not on the line

00:50 Let's move to this point

01:01 Not possible, therefore the point is not on the line

01:05 Let's move to this point

01:15 Possible, therefore the point is on the line

01:18 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

Through which points does the function below pass?

$y=6(2x+4)+x$

Step-by-step solution

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

Step 1: Simplify the expression for $y = 6(2x+4) + x$ .
Step 2: Calculate $y$ at $x = 0$ .

First, let's simplify the expression for $y$ :

$y = 6(2x + 4) + x$
$= 6 \times 2x + 6 \times 4 + x$
$= 12x + 24 + x$
$= 13x + 24$

Now, let's evaluate $y$ when $x = 0$ :

$y = 13(0) + 24$
$= 0 + 24$
$= 24$

This means the function passes through the point $(0, 24)$ . Therefore, the solution to the problem is $(0, 24)$ .

Final Answer

$(0,24)$

Key Points to Remember

Essential concepts to master this topic

Distribution Rule: Apply distributive property before combining like terms
Technique: 6(2x + 4) = 12x + 24, then add x
Check: Substitute x = 0: 13(0) + 24 = 24 ✓

Common Mistakes

Avoid these frequent errors

Forgetting to distribute to all terms inside parentheses
Don't multiply 6 × 2x = 12x and forget the 6 × 4 = 24! This gives y = 12x + x = 13x instead of 13x + 24. Always distribute to every term inside the parentheses before combining like terms.

Practice Quiz

Test your knowledge with interactive questions

Which statement best describes the graph below?

FAQ

Everything you need to know about this question

Do I have to distribute first, or can I substitute x = 0 right away?

You can substitute directly, but distributing first shows the simplified form $y = 13x + 24$ . This makes it easier to find other points and understand the function's behavior.

How do I know which terms to combine?

Look for like terms - terms with the same variable and exponent. Here, 12x and x are like terms, so 12x + x = 13x. The constant 24 stands alone.

What if I need to find where the function passes through other points?

Once you have $y = 13x + 24$ , substitute any x-value you want! For example: when x = 1, y = 13(1) + 24 = 37, so it passes through (1, 37).

Why is the y-intercept important?

The y-intercept (where x = 0) tells you where the line crosses the y-axis. It's the starting point of the linear function and equals the constant term after simplifying.

Can I check my answer using a different x-value?

Absolutely! Try x = 1: Original equation gives $y = 6(2(1) + 4) + 1 = 6(6) + 1 = 37$ . Simplified form gives $y = 13(1) + 24 = 37$ ✓

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