Identify the Function: Graph That Passes Through (5,25)

Q: Do I need to substitute both x and y values?

You only substitute the x-value into each equation, then check if you get the correct y-value. The point (5,25) means when x = 5, y should equal 25.

Q: What if multiple equations seem to work?

Only one equation will give you exactly y = 25 when x = 5. Double-check your arithmetic - each calculation should give a different result.

Q: Should I simplify expressions like 4x + x first?

Yes! Always combine like terms first: $ 4x + x = 5x $. This makes substitution easier and reduces calculation errors.

Q: How do I know which answer choice is correct?

Test each equation by substituting x = 5. The correct equation will give you exactly y = 25. All others will give different y-values.

Q: What if I get the wrong y-value?

That means the equation doesn't pass through the given point. Try the next equation until you find one that gives y = 25 when x = 5.

Function Identification with Point Verification

Choose the graph of the function that passes through the point $(5,25)$

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Find which line contains the point

00:03 In each point, the left number represents the X-axis and the right number represents Y

00:06 Substitute the point in each line equation and check if it's possible

00:15 Not possible, therefore the point is not on this line

00:18 Let's use the same method and find which line contains the point

00:22 Substitute in this line and check if it's possible

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

00:34 Substitute in this line and check if it's possible

00:43 Possible, therefore the point is on this line

00:46 Substitute in this line and check if it's possible

00:52 Not possible, therefore the point is not on this line

00:57 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

Choose the graph of the function that passes through the point $(5,25)$

Step-by-step solution

To solve the problem, let's analyze each equation to determine which function's graph passes through the point $(5, 25)$ .

Equation 1: $y = 4x + 1$
Substitute $x = 5$ into equation: $y = 4(5) + 1 = 20 + 1 = 21$
This does not satisfy $y = 25$ .
Equation 2: $y = 5x + x$
Substitute $x = 5$ into equation: $y = 5(5) + 5 = 25 + 5 = 30$
This does not satisfy $y = 25$ .
Equation 3: $y = 4x + x$
Substitute $x = 5$ into equation: $y = 4(5) + 5 = 20 + 5 = 25$
This satisfies $y = 25$ .
Equation 4: $y = 3x + x$
Substitute $x = 5$ into equation: $y = 3(5) + 5 = 15 + 5 = 20$
This does not satisfy $y = 25$ .

Upon evaluating all the options, Equation 3, $y = 4x + x$ , is the only one that satisfies the condition $y = 25$ when $x = 5$ . Therefore, the function whose graph passes through the point $(5, 25)$ is $y = 4x + x$ .

Final Answer

$y=4x+x$

Key Points to Remember

Essential concepts to master this topic

Point Substitution: Replace x and y with given coordinate values
Technique: Substitute x = 5: y = 4(5) + 5 = 25
Check: Only the correct function yields the exact y-value from coordinates ✓

Common Mistakes

Avoid these frequent errors

Not simplifying expressions before substitution
Don't leave expressions like y = 4x + x unsimplified = harder calculations! Students often substitute without combining like terms first, leading to calculation errors. Always simplify to y = 5x before substituting values.

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 need to substitute both x and y values?

You only substitute the x-value into each equation, then check if you get the correct y-value. The point (5,25) means when x = 5, y should equal 25.

What if multiple equations seem to work?

Only one equation will give you exactly y = 25 when x = 5. Double-check your arithmetic - each calculation should give a different result.

Should I simplify expressions like 4x + x first?

Yes! Always combine like terms first: $4x + x = 5x$ . This makes substitution easier and reduces calculation errors.

How do I know which answer choice is correct?

Test each equation by substituting x = 5. The correct equation will give you exactly y = 25. All others will give different y-values.

What if I get the wrong y-value?

That means the equation doesn't pass through the given point. Try the next equation until you find one that gives y = 25 when x = 5.

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