Math Problem Statement

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. Question content area bottom Part 1 yequals=enter your response here ​(Simplify your​ answer.)

Solution

We are given the following relationships:

  1. m=4n+2m = 4n + 2
  2. y=2m+2y = -2m + 2

We need to express yy as a function of nn.

Step 1: Substitute m=4n+2m = 4n + 2 into the equation for yy

y=2m+2y = -2m + 2 Substitute m=4n+2m = 4n + 2 into the equation for yy: y=2(4n+2)+2y = -2(4n + 2) + 2

Step 2: Simplify the equation

Distribute the 2-2 inside the parentheses: y=2(4n)2(2)+2y = -2(4n) - 2(2) + 2 y=8n4+2y = -8n - 4 + 2 Now, simplify further: y=8n2y = -8n - 2

Thus, yy as a function of nn is: y=8n2y = -8n - 2

Would you like more details or have any questions?


Here are 5 related questions:

  1. How can we graph y=8n2y = -8n - 2 on a coordinate plane?
  2. If n=3n = 3, what is the value of yy?
  3. What is the slope of the function y=8n2y = -8n - 2?
  4. How does the function y=8n2y = -8n - 2 compare to y=4n+2y = 4n + 2?
  5. Can you find the value of mm when n=5n = 5?

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

Ask a new question for Free

By Image

Drop file here or Click Here to upload

Math Problem Analysis

Mathematical Concepts

Algebra
Linear Functions
Substitution

Formulas

y = -2m + 2
m = 4n + 2

Theorems

-

Suitable Grade Level

Grades 8-10