Time Distance Distance / Time
2hrs 90 miles 90 miles / 2 hrs = 45 miles / hr
3hrs 135 miles 135 miles / 3 hrs = 45 miles / hr
5hrs 225 miles 225 miles / 5 hrs = 45 miles / hr
6hrs 270 miles 270 miles / 6 hrs = 45 miles / hr
Constant of proportionality is 45 miles / hr. This is the same for the four values. The unit rate is also 45 miles / hr.
Let us assume the Distance , d is directly proportional to Time, t
d α t
d = kt
Constant of proportionality is k which is D/T
d = 45t
(2,2), you can verify this by doing the midpoint formula (which i forgot) or drawing a graph
We know that the formula for the area of a rectangle is:
We know that the area is 165. Now we need to solve for the dimensions.
Let the width of the rectangle be "

"
Then the length of the rectangle is
Substitute.
Multiply the terms.
Bring the 156 over.
We have to use the quadratic formula to solve this now. Let us restate it:

Now I'm going to fast forward this because all the rest is boring stuff and substitution. The answer is:

Since we cannot have a negative answer, we must cancel out the other answer, which I did not include.
Hope this helped! :)
~Cam943, Junior Moderator
The equation we have right now is basically y = 1/2x + 3. We can switch the x and y variables. Our new equation is: x = 1/2y + 3. Next, we solve for y.
Firstly, we subtract 3 from both sides. This gives us x - 3 = 1/2y. Next, we multiply both sides by 2 to isolate y. This gives us 2(x - 3) = 1/2y. Then, we have 2x - 6 = y.
The answer is f(x) = 2x - 6