How do you find the slope of a line perpendicular to M(2, -1), N(0, 4)?

The slope of the line MN is obtained by:

the slope of a line perpendicular to MN is given by

To find the slope of a line perpendicular to the line passing through points M(2, -1) and N(0, 4), first find the slope of the line passing through M and N using the formula:

[ m = \frac{y_2 - y_1}{x_2 - x_1} ]

Substitute the coordinates of M and N into the formula:

[ m = \frac{4 - (-1)}{0 - 2} ]

[ m = \frac{5}{-2} ]

[ m = -\frac{5}{2} ]

The slope of the line passing through M and N is -5/2.

To find the slope of a line perpendicular to this line, use the fact that the product of the slopes of perpendicular lines is -1. Therefore, the slope of the perpendicular line is the negative reciprocal of -5/2:

[ m_{\text{perpendicular}} = -\frac{1}{m} = -\frac{1}{-5/2} = \frac{2}{5} ]

So, the slope of the line perpendicular to the line passing through M(2, -1) and N(0, 4) is 2/5.