Solve y = (2/5)x + 2 When x Equals 2: Linear Equation

Q: Why do I need to convert the fraction to a decimal?

You don't have to convert to decimal, but it often makes the final calculation easier. $ \frac{4}{5} + 2 = \frac{4}{5} + \frac{10}{5} = \frac{14}{5} = 2.8 $ gives the same result!

Q: What if I get confused about which number to substitute?

Always look for the given information carefully. The problem says "when x = 2", so replace every x in the equation with 2. Don't substitute for y!

Q: How do I multiply a fraction by a whole number?

Multiply the numerator by the whole number: $ \frac{2}{5} \cdot 2 = \frac{2 \cdot 2}{5} = \frac{4}{5} $. The denominator stays the same!

Q: Can I leave my answer as a mixed number?

For this type of problem, decimal form is usually preferred since the answer choices are in decimal format. Convert $ 2\frac{4}{5} $ to 2.8 to match.

Q: What's the difference between this and solving for x?

Here we're evaluating the equation (finding y when x is known). Solving for x means finding what value of x makes the equation true for a given y value.

Linear Equations with Fraction Substitution

Find $y$ when $x=2$

$y=\frac{2}{5}x+2$

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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

00:07 Substitute the X value according to the given

00:17 Raise the product to the numerator

00:21 Calculate the product

00:27 Convert from fraction to decimal

00:37 Insert this decimal fraction in the exercise and continue solving

00:47 Let's sum up

00:52 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

Find $y$ when $x=2$

$y=\frac{2}{5}x+2$

Step-by-step solution

In this exercise, we are given the value of X, so we will substitute it into the formula.

It's important to remember that between an unknown and a number there is a multiplication sign, therefore:

$y=\frac{2}{5}\cdot(2)+2$

$y=\frac{4}{5}+2$

Let's convert to a decimal fraction:

$y=0.8+2$
$y=2.8$

And that's the solution!

Final Answer

$2.8$

Key Points to Remember

Essential concepts to master this topic

Substitution Rule: Replace the variable with the given value directly
Technique: Calculate $\frac{2}{5} \cdot 2 = \frac{4}{5} = 0.8$ before adding
Check: Substitute x = 2 back: $\frac{2}{5}(2) + 2 = 2.8$ ✓

Common Mistakes

Avoid these frequent errors

Forgetting to multiply the fraction by the substituted value
Don't just replace x with 2 and write $y = \frac{2}{5} \cdot 2 + 2$ without calculating = leaves the problem unsolved! This means you haven't actually found the value of y. Always complete the multiplication: $\frac{2}{5} \cdot 2 = \frac{4}{5} = 0.8$ first.

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 need to convert the fraction to a decimal?

You don't have to convert to decimal, but it often makes the final calculation easier. $\frac{4}{5} + 2 = \frac{4}{5} + \frac{10}{5} = \frac{14}{5} = 2.8$ gives the same result!

What if I get confused about which number to substitute?

Always look for the given information carefully. The problem says "when x = 2", so replace every x in the equation with 2. Don't substitute for y!

How do I multiply a fraction by a whole number?

Multiply the numerator by the whole number: $\frac{2}{5} \cdot 2 = \frac{2 \cdot 2}{5} = \frac{4}{5}$ . The denominator stays the same!

Can I leave my answer as a mixed number?

For this type of problem, decimal form is usually preferred since the answer choices are in decimal format. Convert $2\frac{4}{5}$ to 2.8 to match.

What's the difference between this and solving for x?

Here we're evaluating the equation (finding y when x is known). Solving for x means finding what value of x makes the equation true for a given y value.

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