Math Problem Statement

Use the two given functions to write y as a function of x.

yequals

negative 2anegative 1

​,

aequals

negative 5xplus 4

Solution

To write yy as a function of xx, we need to substitute the given expression for aa into the equation for yy.

Step 1: Write down the given equations

  1. y=2a1y = -2a - 1
  2. a=5x+4a = -5x + 4

Step 2: Substitute aa into yy

Substitute a=5x+4a = -5x + 4 into y=2a1y = -2a - 1:

y=2(5x+4)1y = -2(-5x + 4) - 1

Step 3: Simplify the expression

Distribute 2-2 across 5x+4-5x + 4: y=10x81y = 10x - 8 - 1

Combine like terms: y=10x9y = 10x - 9

Final Answer:

y=10x9y = 10x - 9

Would you like me to expand this further or explain the process in more detail?

Here are some related questions you might consider:

  1. How do we verify if this function is correct?
  2. Can you graph y=10x9y = 10x - 9 to visualize its slope and intercept?
  3. What happens to yy if xx is a specific value, like 2 or -3?
  4. How do you determine the domain and range of y=10x9y = 10x - 9?
  5. How would the result change if aa were a different function of xx?

Tip: Always double-check substitutions and algebraic simplifications to avoid errors!

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Math Problem Analysis

Mathematical Concepts

Substitution
Simplification
Linear Equations

Formulas

y = -2a - 1
a = -5x + 4

Theorems

Distributive Property
Linear Equation Theory

Suitable Grade Level

Grades 8-10