Calculating y When x Is 2 in the Equation y = 1/2x

Q: Why isn't the answer just 1/2?

The 1/2 is a coefficient that gets multiplied by x. When x = 2, you calculate $ \frac{1}{2} \times 2 = 1 $. The coefficient alone is never the final answer!

Q: What does it mean to substitute x = 2?

Substitution means replacing every x in the equation with the number 2. So $ y = \frac{1}{2}x $ becomes $ y = \frac{1}{2} \times 2 $.

Q: How do I multiply fractions by whole numbers?

Multiply the numerator by the whole number, keep the denominator the same. So $ \frac{1}{2} \times 2 = \frac{1 \times 2}{2} = \frac{2}{2} = 1 $.

Linear Functions with Substitution

Find a y when x=2

$y=\frac{1}{2}x$

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:06 Let's find why, given the value of X. So, are you ready?

00:11 First, set the X value based on the data we have. Great job!

00:18 Now, let's calculate the quotient carefully. Almost there!

00:23 And that's how we solve the problem. Well done, everyone!

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

Find a y when x=2

$y=\frac{1}{2}x$

Step-by-step solution

To solve this problem, we will follow these steps:

Step 1: Substitute the given value of $x$ into the equation.
Step 2: Perform the calculations to find $y$ .

Now, let's work through each step:
Step 1: The equation provided is $y = \frac{1}{2}x$ . We need to find the value of $y$ when $x = 2$ .
Step 2: Substitute $x = 2$ into the equation:

$y = \frac{1}{2} \times 2$

Simplifying this expression gives:

$y = \frac{2}{2}$

Therefore,

$y = 1$ .

The calculated value of $y$ is $1$ .

Final Answer

$1$

Key Points to Remember

Essential concepts to master this topic

Substitution: Replace x with the given value in the equation
Technique: Calculate $\frac{1}{2} \times 2 = \frac{2}{2} = 1$
Check: Verify y = 1 makes the original equation true ✓

Common Mistakes

Avoid these frequent errors

Confusing the coefficient with the answer
Don't think y equals 1/2 just because you see 1/2 in the equation = wrong answer! The 1/2 is multiplied by x, not the final result. Always substitute the x-value and complete the multiplication.

Practice Quiz

Test your knowledge with interactive questions

Calculate y given that $$ x=2 $$ and $$ y=x $$ .

FAQ

Everything you need to know about this question

Why isn't the answer just 1/2?

The 1/2 is a coefficient that gets multiplied by x. When x = 2, you calculate $\frac{1}{2} \times 2 = 1$ . The coefficient alone is never the final answer!

What does it mean to substitute x = 2?

Substitution means replacing every x in the equation with the number 2. So $y = \frac{1}{2}x$ becomes $y = \frac{1}{2} \times 2$ .

How do I multiply fractions by whole numbers?

Multiply the numerator by the whole number, keep the denominator the same. So $\frac{1}{2} \times 2 = \frac{1 \times 2}{2} = \frac{2}{2} = 1$ .

Can I check my answer?

Yes! Substitute your y-value back: if y = 1 and x = 2, then $1 = \frac{1}{2} \times 2 = 1$ . Since both sides equal 1, your answer is correct!

What if x was a different number?

The same process works! For any x-value, substitute it into $y = \frac{1}{2}x$ and multiply. Try x = 4: $y = \frac{1}{2} \times 4 = 2$ .

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