Write the equation for the following relation. q= {(x, y): (4,5), (8,7), (12,9), (16,}

There's really no way to solve this problem apriori (unless you can use tools like lagrange polynomials to interpolate points), so I'll just tell you how to approach problems like this.

First of all, we may try to see if the dependence is linear: the input is always increased by 4 (4, 8, 12, 16,...) and the output increases by 2: (5, 7, 9, 11). So, the answer is yes.

Now that we know that these points lay on a line, we can conclude the exercise in several ways:

Plug in two points of your choice and you'll get the same answer.

Of course, as a third alternative, you could just have eyeballed the the fact that x grows twice as fast as y could have hinted the x/2 part, and then you could have seen that y is always 3 more than half of x, again leading to y=x/2+3.

y=mx+b

step-by-step explanation:

m is slope, b is y-intercept

use an equation of ratios to determine the amount of gas needed to fill the tank.

    0.2             0.8

  =    

288.75             x

                                                              231 gal

so, 0.2x = (0.8)(288.75 gal), and x = = 1155 gal.

                                                                0.2

it would take 1155 gal. to fill the tank.

the cost would be

1155 gal         $3

* = $3465   (answer)

      1           1 gal

hope this you