In this question, we have to find the slope of the perpendicular line to the graph of the point (-3,-1) and (0,-4).
For that, first, find the slope of the given line.
The slope (m) is calculated by the difference of y values over the x.
m = (y2 - y1)/ (x2 - x1)
Here, the points are:
(-3 , -1)
x1 = -3
y1 = -1
similarly, in (0, -4)
x2 = 0
y2 = -4
Now, put these values in the given equation.
m = (-4 - (-1)) / (0 - (-3))
m = (-4 + 1) / (0+3)
m = -3/ 3
m = -1
Now, the perpendicular slopes are negative reciprocals of each other.
For example, for a given line of slope 'x', the slope of the perpendicular line would be -1/x.
The negative reciprocal of -1 is -1/(-1) = 1.
Hence, the slope of the perpendicular line to the graph of the point (-3,-1) and (0,-4) would be 1.