The table below shows how much joe earns, y, after working x hours. joe’s earnings hours worked money earned 4 $30 10 $75 12 $90 22 $165 the relationship between money earned and hours worked is linear. joe computes the slope between (4, 30) and (12, 90), then computes the slope between (4, 30) and (10, 75). how do the two slopes compare?

Both slopes have the same value which is 7.5.

To compute for the slope we will use this formula:
   m = y^2 - y^1 over x^2 - x^1

For the first slope, the points are (4, 30) and (12, 90). Substitute and simplify.
   m = (90 - 30) over (12 - 4)
   m = 7.5

For the second slope, the points are (4, 30) and (10, 75). Same with the above computation.
   m = (75 - 30) over (10 - 4)
   m = 7.5

Since the relationship is linear, the slope does not change.