What is the y-intercept of the line perpendicular to y= -5/2x + 4/5 including point (-3,-1) ?

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 -5/2, which means that the slope of a line perpendicular to this one, needs to be 2/5. 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 the slope
-1=-3(2/5)+b          Combine like terms
-1=-6/5+b               Add 6/5 in both sides to isolate b
1/5=b
The equation of the line perpendicular to y=-5/2x+4/5 and that passes through the point (-3,-1) is y=2/5x+1/5, and the y-intercept is 1/5 or 0.2.