Final answer:
To have integer x-intercept and y-intercept, k must be a multiple of 15.
Step-by-step explanation:
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.