Video: Creating and Using Linear Equations in More Than One Variable

A plumber charges $40 for a call-out and $60 per hour of labor. Write an equation for 𝑐, the cost of a job, in dollars, which takes 𝑡 hours. What is the cost of a job which takes 3 hours?

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Video Transcript

A plumber charges 40 dollars for a call-out and 60 dollars per hour of labor. Write an equation for 𝑐, the cost of a job, in dollars, which takes 𝑡 hours.

So, this is the first part of the question. There’s also another part we’ll come onto in a bit. But we’re looking first out the information we have. So, we’ve got the fact that the plumber charges 40 dollars for a call-out, 60 dollars per hour for the labor. And the things that we have are 𝑐 is the cost of the job, and 𝑡 is the number of hours it takes. Well, with this question, we can think of it as a linear relationship or model it as if we were using a line, a straight line.

And that is, the 40 dollars would be our 𝑦-intercept because that’s the call-out charge cause what it would mean is that it doesn’t matter if we have zero hours’ work. The second the plumber starts doing any work at all, then it’s gonna cost 40 dollars. So, it will cross the 𝑦-axis at that point. And our slope would be 60 dollars. And that’s because we know that every hour that the plumber works, it will go up by 60 dollars each time. So, if we modeled it as a straight line on a graph, it’d look a bit like this, like I said with our 𝑦-intercept at 40. But what we want to do is write an equation for 𝑐, the cost of a job in dollars, and then which takes 𝑡 hours.

Well, what we can use to write our equation is the general form for the equation of a straight line, which is 𝑦 equals 𝑚𝑥 plus 𝑏. And in our equation, our 𝑦 is gonna be 𝑐 because that’s our cost, and our 𝑥 is gonna be 𝑡 which is our time. Well, as we’ve already identified our slope and 𝑦-intercept, we can write our equation as 𝑐 equals 60𝑡 plus 40. So that’s our equation for 𝑐, the cost of a job in dollars, which takes 𝑡 hours.

So great, that’s the first part of the question answered. Let’s look at the second part.

What is the cost of a job which takes three hours?

Now, all we need to do here is substitute our value three for our 𝑡 into the equation that we formed in the first part of the question. So, when we do that, we’re gonna get 𝑐, the cost of the job which takes three hours, is equal to 60 multiplied by three, because our 𝑡 is three, plus 40. Which is gonna be equal to 180 plus 40, which is gonna to be equal to 220. So therefore, we can say that the cost of a job which takes three hours is 220 dollars.

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