If m is 4 times n plus 2 and y is negative −2 times m plus 2​, then write y as a function of n.
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Part 1
yequals=enter your response here
​(Simplify your​ answer.)

We are given the following relationships:

1. \( m = 4n + 2 \)
2. \( y = -2m + 2 \)

We need to express \( y \) as a function of \( n \).

### Step 1: Substitute \( m = 4n + 2 \) into the equation for \( y \)
\[
y = -2m + 2
\]
Substitute \( m = 4n + 2 \) into the equation for \( y \):
\[
y = -2(4n + 2) + 2
\]

### Step 2: Simplify the equation
Distribute the \( -2 \) inside the parentheses:
\[
y = -2(4n) - 2(2) + 2
\]
\[
y = -8n - 4 + 2
\]
Now, simplify further:
\[
y = -8n - 2
\]

Thus, \( y \) as a function of \( n \) is:
\[
y = -8n - 2
\]

Would you like more details or have any questions?

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Here are 5 related questions:
1. How can we graph \( y = -8n - 2 \) on a coordinate plane?
2. If \( n = 3 \), what is the value of \( y \)?
3. What is the slope of the function \( y = -8n - 2 \)?
4. How does the function \( y = -8n - 2 \) compare to \( y = 4n + 2 \)?
5. Can you find the value of \( m \) when \( n = 5 \)?

**Tip:** Always check your substitutions carefully to avoid mistakes in solving.

If m is 4 times n plus 2 and y is negative −2 times m plus 2, then write y as a function of n.

Learn how to express y as a function of n, given m = 4n + 2 and y = -2m + 2. This problem covers key algebraic concepts, including substitution and linear functions. Suitable for students in Grades 8-10.

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