A tank has 900 liters and leaks 15 liters per hour. 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 tank has 900 liters and leaks 15 liters per hour.

Write the equation.

The liters left depends on the number of hours.

So x is the hours: the input.

y is the liters left: the output.

x = hours, y = liters left

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

Each hour, it goes down by 15.

So m is −15.

= m = −15

Careful!

It leaks 15 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 hours, it is 900.

= b = 900

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 = −15x + 900.

= y = −15x + 900

Let's check with 4 hours: the equation gives 840.

In the story: 900, minus 15, minus 15, minus 15, minus 15: 840.

So the answer is right!

x = 4: −15 × 4 + 900 = 840

Let's look back.

First: which depends on which.

Then: rate of change.

Then: start value.

Then: write the equation.

Last: check.

Answer

= y = −15x + 900

Try this one yourself, then check:

Show the answer

y = −19x + 896