Write AN equAtioN for the live that passes through the given point ANd is Ponadiati to the graph of the given equation

Question

y=-2 -1 , (2 , -1)

Answer 1

for the given line of y = -2x - 1, the slope is m = -2. that means that the slope of the perpendicular line will be the opposite reciprocal, which for this line is

m = -1 / -2 = 1/2

if you plug that slope and the given point into the point-slope form you can solve for the end value

y - y1 = m(x - x1)

y - -1 = 1/2(x - 2)

y + 1 = 1/2x - 1

y = 1/2x - 2

Answer 2

Maddie S. Thank you for this common math problem in Algebra 1.

When finding an equation that is perpendicular to the given equation, it is important to know a few tips.

Your example: y = -2x - 1 through points (2, -1)

The perpendicular slope is the negative reciprocal of the slope in the example given, so in this case the reciprocal of this slope -2 is 1/2. Steps: take original slope and multiply by (-1)(-1/2) = 1/2

Through points (2, -1) means substitute these points for x = 2, y = -1 in the equation.

Rewrite original equation: y = -2x -1 is now y = 1/2x -1; Check: does this pass through points (2, -1)?

Answer 3

If the equation of the line is y = -2x -1, the slope of this line is -2.

A line parallel to this would also have a slope of m = -2.

Starting in point-slope form with the ordered pair (2, -1)

y - (-1) = -2(x -2) *distribute

y+1 = -2x +4 *bring like terms together by subtracting one from each side

y = -2x +3

A line perpendicular to this would have an opposite reciprocal slope of m = 1/2.

Starting in point-slope form with the ordered pair (2, -1)

y - (-1) = 1/2(x -2) *distribute

y+1 = 1/2x -1 *bring like terms together by subtracting one from each side

y = 1/2x -2