One line passes through the points (−3,−1) and (1,−9). Another line passes through points (1,4) and (5,6). Are the lines parallel, perpendicular, or neither?

the two lines are perpendicular to one another

Step-by-step explanation:

Find the slopes of the two lines and then compare them.

If the slopes are the same, the lines are parallel.

If the slopes are negative reciprocals, the lines are perpendicular.

If neither of these conditions hold, then the lines are neither parallel nor perpendicular.

(−3,−1) and (1,−9):  As we go from the first point to the second, x (the "run") increases by 4 and y (the "rise") decreases by 8.  Thus, the slope of the line through (−3,−1) and (1,−9) is m = rise / run = -8/4, or m = -2.

(1,4) and (5,6):  As we go from the first to the second, x increeases by 4 and y increases by 2.  Thus, the slope of the line through (1,4) and (5,6) is

m = rise / run = 2/4 = 1/2.

Because 1/2 is the negative reciprocal of -2, we know that the two lines are perpendicular to one another.

f(x) has value 150 at x= 0

and 0 at x= 3

so d(f(x))/dt = slope = -150/3 = -50