What is the slope of the line that is perpendicular to the line represented by the equation below?
4x - 5y = -1
A. 4/5
B. -4/5
C. 5/4
D. -5/4
is this c or d? reiny, i used what you said, but since this is subtraction i was unsure of whether or not it would be negative or not.
5 y = 4 x + 1
so
y = (4/5) x + 1/5
slope = 4/5
so slope of perpendicular = -5/4
To find the slope of a line perpendicular to a given line, you need to determine the slope of the given line first. The equation of the given line is 4x - 5y = -1.
To determine the slope of this line, you can rewrite the equation in slope-intercept form, which is y = mx + b, where m represents the slope. To do this, solve the equation for y:
-5y = -4x - 1
y = (4/5)x + 1/5
Now you can see that the slope of the given line is (4/5).
Since the line perpendicular to this line has a slope that is the negative reciprocal of (4/5), you need to find the negative reciprocal of (4/5).
To find the negative reciprocal, simply flip the fraction and change the sign. The reciprocal of (4/5) is (5/4), and the negative reciprocal is (-5/4).
Therefore, the slope of the line perpendicular to the given line is -5/4. So, the correct answer is (D).