Consider the equation 3x + 5y = k. What values could k have so that the x-intercept and the y-intercept of the equation’s graph would both be integers? Explain.

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asked Jul 1, 2020 192k views

1 Answer

Rasmita Dash · Answer 1 · 2020-07-07T06:03:24+0000

To have integer x-intercept and y-intercept, k must be a multiple of 15.

To find the x-intercept, we set y = 0 in the equation 3x + 5y = k and solve for x:

3x + 5(0) = k

3x = k

x = k/3

Since the x-intercept needs to be an integer, k must be a multiple of 3.

To find the y-intercept, we set x = 0 in the equation 3x + 5y = k and solve for y:

3(0) + 5y = k

5y = k

y = k/5

Since the y-intercept needs to be an integer, k must be a multiple of 5.

Therefore, values of k that would make both the x-intercept and y-intercept integers must be multiples of both 3 and 5, which are multiples of 15.