Question

Find the equation of a line perpendicular toy, minus, 6, equals, minus, one fifth, xy−6=−

5
1
​
xthat passes through the point left bracket, minus, 2, comma, minus, 4, right bracket(−2,−4).
Answer
Multiple Choice Answers
y, minus, 4, equals, one fifth, left bracket, x, plus, 2, right brackety−4=
5
1
​
(x+2)
y, plus, 4, equals, 5, left bracket, x, plus, 2, right brackety+4=5(x+2)
y, plus, 4, equals, one fifth, left bracket, x, plus, 2, right brackety+4=
5
1
​
(x+2)
y, minus, 4, equals, 5, left bracket, x, minus, 2, right brackety−4=5(x−2)

Answer 1

To find the equation of a line perpendicular to xy-6=-5x and passes through (-2, -4), use the point-slope formula with the slope of -5x. The equation of the perpendicular line is y+4 = 1/5(x+2).

Step-by-step explanation:

To find the equation of a line perpendicular to xy-6=-5x that passes through the point (-2, -4), we first need to determine the slope of the given line. The given line is already in the form y=mx+b, where m represents the slope.

Comparing with the equation xy-6=-5x, we have m=-5.

The slope of a line perpendicular to the given line is the negative reciprocal of the slope of the given line. Therefore, the slope of the perpendicular line is m=1/5.

Substituting the slope m=1/5 and the point (-2, -4) into the point-slope formula y-y1=m(x-x1), we get y- (-4) = 1/5(x-(-2)). Simplifying this equation gives us the equation of the line perpendicular to the given line: y+4 = 1/5(x+2).