Find the Linear Function with Slope 6y Through Point (6,41)

Q: Why doesn't my equation match any of the answer choices?

Your equation might be algebraically equivalent but written differently! Try factoring out common terms. For example, $ y = 6x + 5 $ equals $ y = 2(3x + 2.5) $ when you factor out 2.

Q: How do I convert 2.5 to a mixed number?

2.5 = 2½ because 0.5 = ½. When working with decimals in answer choices, remember that 2.5 and 2½ mean exactly the same thing!

Q: What if I made an arithmetic error finding b?

Double-check your substitution: $ 41 = 6 \times 6 + b $ means $ 41 = 36 + b $, so $ b = 41 - 36 = 5 $. Always verify each step!

Q: Can I check my answer by plugging in the point?

Absolutely! Substitute $ x = 6 $ into your final equation. For $ y = 2(3x + 2.5) $: $ y = 2(3(6) + 2.5) = 2(18 + 2.5) = 2(20.5) = 41 $ ✓

Linear Functions with Point-Slope Applications

A straight line has a slope of 6y and passes through the points $(6,41)$ .

Which function corresponds to the line described?

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Find the algebraic representation for the function

00:03 We'll use the straight line equation

00:09 We'll substitute the point according to the given data

00:13 We'll substitute the line's slope according to the given data

00:21 We'll continue solving to find the intersection point

00:29 We'll isolate intersection point B

00:37 This is the intersection point with the Y-axis

00:46 Now we'll substitute the intersection point and slope in the line equation

00:54 We'll factor 6 into 2 and 3

01:06 We'll factor 5 into 2 and 2.5

01:14 We'll factor out the common term from the parentheses

01:21 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

A straight line has a slope of 6y and passes through the points $(6,41)$ .

Which function corresponds to the line described?

Step-by-step solution

To solve the exercise, we will start by inserting the available data into the equation of the line:
y = mx + b
41 = 6*6 + b
41 = 36 +b
41-36 = b
5 = b

Now we have the data for the equation of the straight line:

y = 6x + 5
But it still does not match any of the given options.

Keep in mind that a common factor can be excluded:
y = 2(3x + 2.5)

Final Answer

$y=2(3x+2\frac{1}{2})$

Key Points to Remember

Essential concepts to master this topic

Point-Slope Form: Use y = mx + b with known slope and point
Technique: Substitute (6,41): 41 = 6(6) + b, so b = 5
Check: Factor common terms: y = 6x + 5 = 2(3x + 2.5) ✓

Common Mistakes

Avoid these frequent errors

Not factoring the final equation to match answer choices
Don't stop at y = 6x + 5 when it doesn't match options = missing the correct answer! The equation might be written in factored form. Always check if you can factor out common terms like 2(3x + 2.5) to match the given choices.

Practice Quiz

Test your knowledge with interactive questions

Look at the linear function represented in the diagram.

When is the function positive?

FAQ

Everything you need to know about this question

Why doesn't my equation match any of the answer choices?

Your equation might be algebraically equivalent but written differently! Try factoring out common terms. For example, $y = 6x + 5$ equals $y = 2(3x + 2.5)$ when you factor out 2.

How do I convert 2.5 to a mixed number?

2.5 = 2½ because 0.5 = ½. When working with decimals in answer choices, remember that 2.5 and 2½ mean exactly the same thing!

What if I made an arithmetic error finding b?

Double-check your substitution: $41 = 6 \times 6 + b$ means $41 = 36 + b$ , so $b = 41 - 36 = 5$ . Always verify each step!

Can I check my answer by plugging in the point?

Absolutely! Substitute $x = 6$ into your final equation. For $y = 2(3x + 2.5)$ : $y = 2(3(6) + 2.5) = 2(18 + 2.5) = 2(20.5) = 41$ ✓

Why is the slope given as '6y' in the problem?

That appears to be a typo in the problem statement. Based on the solution and answer choices, the slope should be 6, not '6y'. Focus on the numerical value 6 for your calculations.

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