Question

write the slope-intercept form of the equation of the line passing through the point (-2,-5) and perpendicular to the line y= 2/3x - 1

Answer 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 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.