What is the equation of a line that is perpendicular to y=4x+5 and passes through the point (8, 3)?

To start, first you must figure out the slope of your perpendicular line which is found by finding the negative reciprocal (switching the numerator and denominator around) of the current slope. Since the current slope is 4, the slope of the line perpendicular to it would be -1/4. Now that you have your slope, you can plug it into the m value of y=mx+b as well as plugging into the x and y values your coordinate point, (8,3). This would look like this:
3=-1/4(8)+b

Since your only missing value now is the b value, or your y-intercept, you must now solve the equation for b. First simplify -1/4(8) which simplifies to -2:
3=-2+b

Then add -2 to both sides to get that b=5. Now that you have the b and m value, you can conclude that your perpendicular equation that passes through (8,3) is y=-1/4x+5
:)