Which line below is perpendicular to 5x+6y=18
?(1 point)
Responses
y=−6/5x+8
y is equal to negative 6 fifths x plus 8
y=5/6x+2
y is equal to 5 sixths x plus 2
y=−5/6x+6/5
y is equal to negative 5 sixths x plus 6 fifths
y=6/5x+3
y is equal to 6 fifths x plus 3
The line perpendicular to 5x+6y=18 would have a slope that is the negative reciprocal of the slope of 5x+6y=18.
The slope of 5x+6y=18 can be found by rearranging the equation into slope-intercept form (y=mx+b):
6y = -5x + 18
y = (-5/6)x + 3
The slope of the line is -5/6.
To find the line that is perpendicular to this, we need to find the negative reciprocal of -5/6, which is 6/5.
Therefore, the line that is perpendicular to 5x+6y=18 will have a slope of 6/5.
The line y=6/5x+3 is the only option with a slope of 6/5, so the correct answer is:
y=6/5x+3
y is equal to 6 fifths x plus 3