Select the Graph of the Function that Passes Through (1/2, 5)

Q: Why do I need to test both x and y values?

A point has two coordinates (x, y). The function must work for both values simultaneously. Testing only one coordinate doesn't prove the point lies on the function!

Q: What if I get different forms of the same equation?

Some equations like $ 4x = y - 3 $ and $ y = 4x + 3 $ are equivalent! Always rearrange to standard form or test the given form directly.

Q: How do I handle fractions when substituting?

Be careful with fraction arithmetic! When substituting $ x = \frac{1}{2} $, multiply step by step: $ 4 \times \frac{1}{2} = \frac{4}{2} = 2 $.

Point Substitution with Function Testing

Choose the graph of the function that passes through the point $(\frac{1}{2},5)$

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:05 Let's find out which line the point is on.

00:09 Remember, the left number is X, and the right is Y.

00:13 We'll substitute the point into each line equation to check.

00:19 This one doesn't work, so the point isn't on this line.

00:23 Let's try the next line equation using the same method.

00:26 Substitute the point and see if it fits.

00:30 No luck here; the point isn't on this line either.

00:34 Let's check another line using the same substitution.

00:42 Still no match; the point isn't here.

00:46 Try one more line and substitute the point.

00:51 It fits! The point is on this line.

00:55 And that's how we find the right line for the point!

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 $(\frac{1}{2},5)$

Step-by-step solution

To solve this problem, we'll proceed by comparing each answer choice through substitution:

Choice 1: $y = -4x$
Substitute $x = \frac{1}{2}$ : $y=-4\times\frac{1}{2}=-2$
Does this equal 5? No, so this choice is incorrect.
Choice 2: $y = 4x$
Substitute $x = \frac{1}{2}$ : $y=4\times\frac{1}{2}=2$
Does this equal 5? No, so this choice is also incorrect.
Choice 3: $y = -4x + 3$
Substitute $x = \frac{1}{2}$ : $y=-4\times\frac{1}{2}+3=-2+3=1$
Does this equal 5? No, this choice is incorrect as well.
Choice 4: $4x = y - 3$
Substitute $x = \frac{1}{2}$ and $y = 5$ : $4 \times \frac{1}{2} = 5 - 3 \$ which simplifies to $2 = 2 \$
This equation holds true with the given point.

Therefore, the solution to the problem is $4x = y - 3$ .

Final Answer

$4x=y-3$

Key Points to Remember

Essential concepts to master this topic

Rule: A function passes through a point when substitution gives true equality
Technique: Substitute x = 1/2 and y = 5 into each equation
Check: Both sides equal when 4(1/2) = 5 - 3 gives 2 = 2 ✓

Common Mistakes

Avoid these frequent errors

Testing only x or only y values
Don't substitute just x = 1/2 and ignore y = 5! This only tests half the point and gives incomplete information. Always substitute both coordinate values to check if the equation balances perfectly.

Practice Quiz

Test your knowledge with interactive questions

Which statement best describes the graph below?

FAQ

Everything you need to know about this question

Why do I need to test both x and y values?

A point has two coordinates (x, y). The function must work for both values simultaneously. Testing only one coordinate doesn't prove the point lies on the function!

What if I get different forms of the same equation?

Some equations like $4x = y - 3$ and $y = 4x + 3$ are equivalent! Always rearrange to standard form or test the given form directly.

How do I handle fractions when substituting?

Be careful with fraction arithmetic! When substituting $x = \frac{1}{2}$ , multiply step by step: $4 \times \frac{1}{2} = \frac{4}{2} = 2$ .

What if none of the equations work?

Double-check your substitution calculations! Make sure you're using the correct point coordinates and following order of operations carefully.

Can I solve this by graphing instead?

Yes! You could plot each function and see which graph contains the point $(\frac{1}{2}, 5)$ . However, algebraic substitution is faster and more precise.

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