Which of the following equations represents a line that is perpendicular to y = -4x + 9 and passes through the point, (4, 5)?

Perpendicular lines refers to a pair of straight lines that intercept each other. The slopes of this lines are opposite reciprocal, meaning that it's multiplication is equal to -1.

In this exercise is given the equation of a line and a point, and is asked to find the equation of the line that is perpendicular to the given one, and that passes through the given point.

The slope of the given line is -4, which means that the slope of a line perpendicular to this one, needs to be 1/4. Now you need to find the value of b or the y-intercept by substituting the given point into the formula y=mx+b, where letter m represents the slope.

y=mx+b                Substitute the values of the given point and slope
5=1/4(4)+b           Combine like terms
5=1+b                  Subtract 1 in both sides to isolate b
4=b

The equation of the line perpendicular to y=-4x+9 and that passes through the point (4,5) is y=1/4+4.