You need at least $40 to buy some notebooks, but your parents don’t want to give you more than $50. Write an inequality representing the possible amount of money you could get.

m = amount of money you receive

You need at least $40, so that means you need m = 40 or more

So which is the same as saying . You flip both sides and also flip the inequality sign as well.

At the same time, your parents won't give you more than $50. So the largest m can get is m = 50. This means

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Combine and to get the compound inequality

This represents all the possible values of m. We see that m can get as small as m = 40, or as large as m = 50, or anything in between.

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The table of  and  is shown below

We start by working out the steepness of the slope (gradient). We can pick any pairs of  from the table

Let choose  and  as  and  respectively

gradient () = 

To form the linear equation, we can use the formula