Question

When analyzing three linear functions Bill notice that they all intercepted the point (10, 10). What conclusion can Bill come to about the linear function with the largest slope?

Answer 1

The function with the largest slope will have the smallest y-intercept.
We know that all functions intercept at (10,10). Because of that, we can write this down:

`y=a_1x+n_1\\ y=a_2x+n_2\\ y=a_3x+n_3\\`
a represents the slope, and n represents the y intercept.

`10=10a_1+n_1\\ 10=10a_2+n_2\\ 10=10a_3+n_3\\`
From this it is pretty obvius that if you have a higher slope you must have smaller y-intercept.