To solve this problem, we can follow the following steps:
Step 1: Convert the given equation into slope-intercept form. The equation -4x + 5y = 1 can be written as y = (4/5)x + 1/5. Now we know the slope of the given line (4/5).
Step 2: Recall that the slope of any line perpendicular to a line is negative reciprocal of the slope of that line. This is a property of perpendicular lines. Hence the slope (m) of the line we are trying to find will be -1 / (4/5) which simplifies to -5/4.
Step 3: We know that the line we're looking for passes through the point (-16,-3). This information will allow us to find the y-intercept of our desired line. The general equation of a line is y = mx + c where m is the slope and c is the y-intercept. We substitute the coordinates of given point and the slope to this equation. Plugging in those values, we get -3 = (-5 / 4) * (-16) + c. Solving this equation will yield the value of c.
Step 4: Therefore, after solving the above equation, we find the y-intercept c to be -23.
So, putting it all together, the equation of the line in slope intercept form that is perpendicular to the given line and passes through the point (-16,-3) is y = -1.25x - 23.