Directions: Using the digits 1 to 9 at most one time each, fill in the boxes to write the equation of a line that passes through the point with the largest possible y-intercept. How many solutions can you find?

### Hint

For a given y-intercept, how do you figure out a possible slope and point?

### Answer

17 possible solutions that have 9 as the y-intercept:

y=-8/1x+9 through (2, -7)

y=-7/1x+9 through (2, -5)

y=-6/1x+9 through (2, -3)

y=-5/1x+9 through (3, -6)

y=-8/2x+9 through (4, -7)

y=-3/1x+9 through (5, -6)

y=-6/2x+9 through (4, -3)

y=-4/2x+9 through (5, -1)

y=-6/3x+9 through (5, -1)

y=-8/4x+9 through (5, -1)

y=-2/1x+9 through (6, -3)

y=-4/2x+9 through (6, -3)

y=-8/4x+9 through (6, -3)

y=-2/1x+9 through (7, -5)

y=-4/2x+9 through (7, -5)

y=-6/3x+9 through (7, -5)

y=-8/4x+9 through (7, -5)

y=-8/1x+9 through (2, -7)

y=-7/1x+9 through (2, -5)

y=-6/1x+9 through (2, -3)

y=-5/1x+9 through (3, -6)

y=-8/2x+9 through (4, -7)

y=-3/1x+9 through (5, -6)

y=-6/2x+9 through (4, -3)

y=-4/2x+9 through (5, -1)

y=-6/3x+9 through (5, -1)

y=-8/4x+9 through (5, -1)

y=-2/1x+9 through (6, -3)

y=-4/2x+9 through (6, -3)

y=-8/4x+9 through (6, -3)

y=-2/1x+9 through (7, -5)

y=-4/2x+9 through (7, -5)

y=-6/3x+9 through (7, -5)

y=-8/4x+9 through (7, -5)

Source: Andy Schwen

Shouldn’t there be a negative with the slope? Also the title says maximum slope, but the directions do not mention that.

LBP–you are correct. It should be in there with some additional instructions. Here is the version I have–might have left some stuff out when I submitted it. Good catch.

https://docs.google.com/drawings/d/17wNJBMkw41cOqUUvGGzo6eX-Nk1VRJNzfiVSsAofV1w

Thanks for this. I will use but just change the domain from 1 – 9 to -9 to +9

Yes. This was very confusing. I did not want to look at the answer but then I figured out the slope MUST be negative for this to work. the directions don’t allow for a negative number:(.

The slope is now showing as negative, and the “max” has been limited to just the y-intercept.