Final answer:
To rewrite the relation 5x + 4y = -2x - 3y as a function of x, isolate y on one side of the equation by moving the terms involving y to the right side and the terms involving x to the left side. The resulting function is y = -x.
Step-by-step explanation:
To rewrite the relation 5x + 4y = -2x - 3y as a function of x, we need to isolate y on one side of the equation. First, let's move the terms involving y to the right side by subtracting 4y from both sides of the equation:
5x + 4y - 4y = -2x - 3y - 4y
5x = -2x - 7y
Next, let's move the terms involving x to the left side by adding 2x to both sides of the equation:
5x + 2x = -2x + 2x - 7y
7x = -7y
Finally, to express y in terms of x, we can divide both sides of the equation by -7 to solve for y:
y = (-7x)/7
y = -x
Therefore, the relation 5x + 4y = -2x - 3y can be rewritten as a function of x: y = -x.