first of I have no idea if I posted this in the right forum. I apologize if I haven't.

how do I find the linear cost equation for the following problem

you will need to buy a power mower for $635. Every time you mow a lawn, you will spend $0.40 on gasoline. You decide to charge a flat rate of $15 dollars for mowing a lawn.

also how can I find the revenue equation.

any help will be appreciated. Thank you

Finding a "cost equation" usually means finding an equation (function, actually) that tells you what your total costs would be at any specified level of activity.

In your example, what is your total cost if you mowed a single lawn? It's the cost of the mower, plus 40 cents on gas, or $635.40.

Ten lawns? $635 + (10 x 0.40) = $639.
15 lawns would be 635 + (15 x 0.40) = 641. You get the drift.

To generalize, if we let C denote your total costs, then your 'cost equation' is

C = 635 + 0.40x

... where x denotes the total number of lawns mowed. (Let me guess.. you've decided to name your biz "Lawn Order"?)

You can see how that equation gives you the total cost of mowing any number x of lawns. The equation just expresses mathematically what you already know--your total cost will always be 40 cents per lawn (gas), plus the price of the mower (which is 635 no matter how many yards you cut).

Cooking up your Revenue equation will follow that same thinking: It'll be the number of lawns mowed, multiplied by the amount charged per job.