Could you please help me with one of my math problem?

Question

Suppose a new watersports company, Aqua Sport, is open for business. They are running a grand opening sale. Their rental cost can be modeled by a linear equation. We are told that for 30 minute of use, their rental will be $50; for 60 min of use, their rental cost will be $80. I have to write an equation that represents the cost, y, to rent a jet ski from Aqua Sports based on the number of minutes, x, that the jet ski is used.

Answer 1

Hi, Dennis,

 

There are two "typical" ways of expressing the equation of a linear function:

 

    the slope-intercept format: y=mx+b, where m is the slope of the line, and b is the y-intercept, and

 

    the point-slope format: (y-y₀)=m(x-x₀), where m is the slope, and (x₀,y₀) is a point on the line.

 

In this case, I think it will be easiest to determine the point-slope format of the line, and then use algebra to turn it into the slope-intercept format, which is the usual format for describing a linear equation.

 

First, the problem basically tells us that when x₁=30min, y₁=$50; and when x₂=60min, y₂=$80. Since slope is equal to rise/run, or (y₂-y₁)/(x₂-x₁):

 

    The slope of this line must be (80-50)/(60-30) = 30/30 = 1

 

    Slope (m) = 1

 

We can pick either of the (x,y) combinations that the problem gives us, to plug into the point-slope equation:

 

    (y-50)=1(x-30)

 

Rearranging to put it into slope-intercept format:

 

    y-50 = x - 30

 

    y = x + 20, where y is the cost, and x is the number of minutes the jet ski is used