If contains the points (4, 19) and (-3, 5), what is the slope of a line perpendicular to ? Enter your answer as a decimal.
To find the slope of a line perpendicular to another line, we need to find the negative reciprocal of the slope of the given line.
Given the points (4, 19) and (-3, 5), we can use the slope formula to find the slope of the line passing through these points.
The slope formula is given by the equation:
m = (y2 - y1) / (x2 - x1)
Let's plug in the coordinates:
m = (5 - 19) / (-3 - 4)
m = (-14) / (-7)
m = 2
So the slope of the given line is 2.
Now, to find the slope of the line perpendicular to this line, we need to take the negative reciprocal of 2.
The negative reciprocal of a number is obtained by taking the negative of the number and then finding its reciprocal (flipping the fraction):
Negative reciprocal of 2 = -1/2
Therefore, the slope of a line perpendicular to the given line is -1/2.