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 -1.
On this case they give you the equation of a line and a point, and is asked to find the y-intercept of the line that is perpendicular to the given one, and that passes through the given point.
The slope of the given line is 2/3, which means that the slope of a line perpendicular to this one, needs to be -3/2. 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=-3/2(-2)+b Combine like terms
-5=3+b Subtract 3 in both sides to isolate b
-8=b
The equation of the line perpendicular to y=2/3x-1 and that passes through the point (-2,-5) is y=-3/2-8.
