what is the slope of the altitude when A(3,-1) B(4,3) C(5,-2) are locations of its vertices
The altitude is the perpendicular line that start from one vertex and falls on the line that passes through the other two vertices.
Hence, supposing that you need to evaluate the slope of the altitude `AD` , where `AD` is the perpendicular line to BC, you need to use the relation between the slopes of two perpendicular lines, such that:
`m_(AD)*m_(BC) = -1 => m_(AD) = -1/(m_(BC))`
You need to evaluate the slope of the line `BC` , using the following formula, such that:
`m_(BC) = (y_C - y_B)/(x_C - x_B)`
`m_(BC) = (-2 - 3)/(5 - 4) => m_(BC) = -5`
`m_(AD) = -1/(m_(BC)) => m_(AD) = -1/(-5) => m_(AD) = 1/5`
Hence, evaluating the slope of the requested altitude, under the given conditions, yields `m_(AD) = 1/5` .