Give two points with integer coordinates that have a slope of 10/7 between them

(0,0) and (7,10)

Step-by-step explanation:

recall that the slope - intercept  form of a linear equation can be given as

y = mx + b

where m = slope and b = y intercept

in our case, we are given that slope, m = 10/7, hence our equation becomes

y = (10/7) x + b

since we are not given any information about the y-intercept, we can simply pick a value for b that is most convenient for us.

We pick b = 0, hence the equation simplifies to:

y = (10/7) x   eq 1

we can see immediately that if x = 0, y must also = 0

proof if x = 0:

y = (10/7)(0) =0

since 0 is an integer, then (0,0) must be the first point.

we can also observe that for y to be an integer, we must get rid of the denominator 7. We can do this by multiply the right side by 7. Hence we let x = 7:

y = (10/7) x 7

y = 10

hence (7,10) is the second point.

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