I wanted to make a test bank of graphs of linear equations for my algebra classes. I want the $y$-intercept of each graph to be an integer no less than $-10$ and no greater than $10$. Generally, you want these graphs to be small, so i've decided on a $20 \times 20$ grid (10 units from the origin). Additionally, i would like students to be able to see a second integral point on this grid, so they can find the slope. How many possible graphs would be in this test bank? How did you get the solution?
Number of distinct graphs with y-intercepts that are integers between $-10$ and $10$
1
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combinatorics
diophantine-equations