What is the slope of a line perpendicular to the line with equation y = 4x + 5?

Hello!

The thing to know what solving problems like these is that slopes of perpendicular lines are opposite reciprocals of each other.

For example, if you are given that the slope of a line is 6, and are told to find the slope of a line perpendicular to it, you would flip the 6/1 to 1/6 and negate it. The slope of a line perpendicular to a line with a slope of 6 is -1/6.

Here, you have an equation of a line in slope-intercept form. Slope-intercept form is y = mx + b, where m is the slope and b is the y-intercept.
In y = 4x + 5, 4 is m, thus 4 is the slope.

The opposite reciprocal of 4 is -1/4.

-1/4