Question

Determine whether the graph of the equation is increasing or decreasing. Write the correct answer before the number. Show your solutions.

5y = x - 2​​

Answer 1

Increasing

Explanation:

We are given the function:

`\displaystyle \large{5y = x - 2}`

Since y is the function of x; we isolate y by dividing both sides by 5.

`\displaystyle \large{ (5y)/(5) = (x - 2)/(5) }`

Thus:

`\displaystyle \large{ y = (x - 2)/(5) }`

Simplify the expression, separating the fraction.

`\displaystyle \large{ y = (x)/(5) - (2)/(5) }`

Familiar with this equation? This function is a linear function.

Now to the increasing and decreasing part. There are several ways to find whether if the graph is increasing.

1. By substituting values
2. Graph Visualization (Or look at the graph)

I will demonstrate the first method. Start from substituting negative to positive, if we keep substituting higher numbers and we get higher y-value then the graph is increasing.

If we substitute higher numbers but we get lower y-value then the graph is decreasing.

Substitution

y = -1/5 - 2/5 = -3/5

y = 0-2/5 = -2/5

y = 1/5-2/5 = -1/5

y = 2/5-2/5 = 0

y = 3/5-2/5 = 1/5

y = 4/5-2/5 = 2/5

y = 5/5-2/5 = 3/5

y = 6/5-2/5 = 4/5

...

As so on, as we see, when x keeps increasing, y increases too.

Therefore, the graph is increasing.