Question

What is the slope of the graph of the solutions for the equation 2,000 = 20x + 10y? Explain how you know.

Answer 1

To determine the slope of a line is best to write the equation on the slope-intercept form.

The general structure of that form is

`y=mx+b`

Where

m is the slope

b is the y-coordinate of the y-intercept

Then to determine the slope of the given equation you have to write it in terms of y

`2000=20x+10y`

Pass the x-term to the other side

`2000-20x=10y`

Divide both sides by 10

`\begin{gathered} (2000)/(10)-(20)/(10)x=(10)/(10)y \\ 200-2x=y \\ y=\text{-}2x+200 \end{gathered}`

From this equation, we can determine that the slope corresponds to the coefficient that multiplies the x-term

`y=-2x+200`

The slope is m=-2