Problem: Same y intercept as x+4y=16, through (4,5)
Y intercept is when x=0 so 4y=16, y=4, y intercept (0,4)
Slope of line through (0,4) and (4,5) is change in y over change in x,
m = (5 - 4)/(4 - 0) = 1/4
Answer: slope 1/4
Check:
The new line is y = (1/4) x + 4
because the y intercept is still (0,4)
Let's check it's through (4,5)
(1/4) (4) + 4 = 5 check