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

00:08 Let's find out which points lie on this line.

00:11 Open the parentheses carefully; multiply each term properly.

00:22 This right here, is the equation of the line.

00:26 Remember, each point has an X value and a Y value.

00:32 We will substitute each point into the equation to see if it works.

00:36 This one doesn't work, so the point is not on the line.

00:40 Let's apply the same method to all the points.

00:44 Now, let's try another point and see what we find.

00:51 Again, it doesn't work, so this point is also not on the line.

00:58 Let's give it one more shot with a different point.

01:09 Unfortunately, this one also doesn't work.

01:13 Try one more point... and yes! This one lies on the line.

01:23 And that's how we find which points are on the line. Good job!

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

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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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