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

Answer:

y = 25x, proportional relationship

Step-by-step 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 $\frac{y_{1} - y_{2}}{x_{1} - x_{2}}$ with any two points, I'm going to use  (2, 50) and (3, 75):

$\frac{y_{1} - y_{2}}{x_{1} - x_{2}} = \frac{50 - 75}{2 - 3} = \frac{-25}{-1} = 25$

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.