Solve y=0.8x: Finding y When x=2 (Linear Equation)

Q: Why do I multiply 0.8 by 2 instead of adding them?

The equation $ y = 0.8x $ means y equals 0.8 times x. The coefficient 0.8 is multiplied by whatever value x has, so when x = 2, we calculate $ 0.8 \times 2 $.

Q: How do I multiply decimals like 0.8 × 2?

Think of it as $ \frac{8}{10} \times 2 = \frac{16}{10} = 1.6 $, or simply multiply 8 × 2 = 16, then place the decimal point one place from the right since 0.8 has one decimal place.

Q: What if I got 16 instead of 1.6?

You forgot about the decimal point! 0.8 has one decimal place, so your answer must also account for this. Always count decimal places carefully when multiplying.

Q: How can I check if 1.6 is the right answer?

Substitute back into the original equation: $ y = 0.8x $ becomes $ 1.6 = 0.8(2) $. Since $ 0.8 \times 2 = 1.6 $, both sides are equal, so your answer is correct!

Q: Is this the same as solving for x when y is given?

No! Here we're substituting a known x-value to find y. If you were solving for x when y is given, you'd divide both sides by 0.8 to isolate x.

Linear Substitution with Decimal Coefficients

Calculate y given that $X=2$ and $y=0.8x$ .

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Find Y according to the given X value

00:04 Substitute the X value according to the given

00:12 Calculate the multiplication

00:17 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

Calculate y given that $X=2$ and $y=0.8x$ .

Step-by-step solution

To solve this problem, we will follow these steps:

Step 1: Identify the given information
Step 2: Apply the formula
Step 3: Perform the calculation

Now, let's work through each step:
Step 1: The problem gives us that $x = 2$ and the relationship between $y$ and $x$ is $y = 0.8x$ .
Step 2: We will use the formula $y = 0.8 \times x$ .
Step 3: Substituting $x = 2$ into the formula, we get $y = 0.8 \times 2$ .

The calculation is as follows:
$y = 0.8 \times 2 = 1.6$ .

Therefore, the solution to the problem is $y = 1.6$ .

Final Answer

1.6

Key Points to Remember

Essential concepts to master this topic

Substitution Rule: Replace the variable with its given value directly
Technique: Calculate $0.8 \times 2 = 1.6$ using decimal multiplication
Check: Verify by substituting back: when x = 2, y = 1.6 ✓

Common Mistakes

Avoid these frequent errors

Confusing variable values or incorrect decimal multiplication
Don't mix up x = 2 with y = 2 or calculate 0.8 × 2 = 0.16! This happens when rushing through decimal placement or confusing which variable has which value. Always clearly identify the given variable and carefully multiply decimals.

Practice Quiz

Test your knowledge with interactive questions

Find a y when $$ x=2 $$

$$ y=5x $$

FAQ

Everything you need to know about this question

Why do I multiply 0.8 by 2 instead of adding them?

The equation $y = 0.8x$ means y equals 0.8 times x. The coefficient 0.8 is multiplied by whatever value x has, so when x = 2, we calculate $0.8 \times 2$ .

How do I multiply decimals like 0.8 × 2?

Think of it as $\frac{8}{10} \times 2 = \frac{16}{10} = 1.6$ , or simply multiply 8 × 2 = 16, then place the decimal point one place from the right since 0.8 has one decimal place.

What if I got 16 instead of 1.6?

You forgot about the decimal point! 0.8 has one decimal place, so your answer must also account for this. Always count decimal places carefully when multiplying.

How can I check if 1.6 is the right answer?

Substitute back into the original equation: $y = 0.8x$ becomes $1.6 = 0.8(2)$ . Since $0.8 \times 2 = 1.6$ , both sides are equal, so your answer is correct!

Is this the same as solving for x when y is given?

No! Here we're substituting a known x-value to find y. If you were solving for x when y is given, you'd divide both sides by 0.8 to isolate x.

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