Question

Use the table to determine whether the relationship is proportional. If so, write an equation for the relationship. Tell what each variable you used represents.

Answer 1

y = 25x, proportional relationship

Explanation:

Let "x" = number of hours read (replace with "h" if that's the variable your teacher wants)

Let "y" = number of pages read (you can use any other variables if you want)

Let's first calculate the slope using
`(y_(1) - y_(2))/(x_(1) - x_(2))` with any two points, I'm going to use (2, 50) and (3, 75):

`(y_(1) - y_(2))/(x_(1) - x_(2)) = (50 - 75)/(2 - 3) = (-25)/(-1) = 25`

Our slope is m = 25.

Now we can use the point-slope form
`y-y_(1) = m(x-x_(1))` with our slope and any point (I'll use (2, 50)) to figure out the equation:

`y-y_(1) = m(x-x_(1)) \\ y-50 = 25(x-2)`

Simplify:

`y-50 = 25(x-2)\\y-50 = 25 x -50\\ y = 25x`

Since the slope is positive, the relationship is proportional.