A pool has 500 liters and drains 20 liters per minute. Write the…

Step by step, with the reason for every step · Equation of a line from a table or a story · Algebra 1

Step by step

Question: A pool has 500 liters and drains 20 liters per minute.

Write the equation.

The liters left depends on the number of minutes.

So x is the minutes: the input.

y is the liters left: the output.

x = minutes, y = liters left

Rate of change means: how much y changes when x goes up by 1.

Each minute, it goes down by 20.

So m is −20.

= m = −20

Careful!

It drains 20 each time.

Going down means a minus.

Careful: going down: m is negative

The start value is y when x is 0.

At the start, with 0 minutes, it is 500.

= b = 500

A line is y = m x plus b: m is the rate of change, b is the start value.

y = mx + b

So the equation is y = −20x + 500.

= y = −20x + 500

Let's check with 4 minutes: the equation gives 420.

In the story: 500, minus 20, minus 20, minus 20, minus 20: 420.

So the answer is right!

x = 4: −20 × 4 + 500 = 420

Let's look back.

First: which depends on which.

Then: rate of change.

Then: start value.

Then: write the equation.

Last: check.

Answer

= y = −20x + 500

Try this one yourself, then check:

Show the answer

y = −18x + 495