Determine which two equations represent perpendicular lines.
a).y=5/3x-5
b).y=5x-5/3
c).y=-1/5x+5/3
d).y=1/5x-5/3
perpenduclar lines have negative reciprocal slopes
y= 3x + 3
y= -1/3 x + 55 are perpendicular lines.
Thanks
To determine which two equations represent perpendicular lines, we need to examine the slopes of the lines represented by the equations.
The slope of a line can be determined by comparing the coefficients of the x-term and y-term in the equation.
If two lines are perpendicular, their slopes must be negative reciprocals of each other. In other words, if the slope of one line is m, the slope of the perpendicular line will be -1/m.
Let's find the slopes of the given equations:
a). y = (5/3)x - 5
The slope of this line is 5/3.
b). y = 5x - (5/3)
The slope of this line is 5.
c). y = (-1/5)x + (5/3)
The slope of this line is -1/5.
d). y = (1/5)x - (5/3)
The slope of this line is 1/5.
Now, we need to compare the slopes to find the negative reciprocals.
The negative reciprocal of 5/3 is -3/5, which is not the slope of any of the other equations.
The negative reciprocal of 5 is -1/5, which is the slope of equation c).
Therefore, the two equations that represent perpendicular lines are a) y = (5/3)x - 5 and c) y = (-1/5)x + (5/3).