Answer
See below.
Work Step by Step
A linear function is even if it is a horizontal line with a slope of $0$, because then it will be symmetric about the y-axis.
A linear function is odd if and only if its y-intercept is 0 and its slope is non-zero. Then the linear function will pass through the origin and $f(-x)=m(-x)=-mx = -f(x)$, which is the requirement to be odd.
