write an equation of the line that is perpendicular to the given line and that passes through the given point

Question

write an equation of the line that is perpendicular to the given line and that passes through the given point y+1=2(x-3); (5,0)

Answer 1

Two lines are perpendicular if the product of their slops is -1. It means given the line L with slop m, any perpendicular line to L has slop - 1/m.

For your question, the slop of perpendicular line to the line y+1= 2(x+5) is -1/2. Now you have the slop and a point of this line. Using point slop formula, you can derive the equation of the line as following:

y - 0 = -1/2 (x-5) which is y = (-1/2) x + 5/2.

Answer 2

If two lines are perpendicular, their slopes are negative reciprocals.

The original problem is in point - slope form (y - y_,) = m (x - x₁), where m is the slope.

So m = 2, so the line perpendicular to it will have a slope, m = -½ or m = -.5

If this line passes through (5, 0), we can find the equation of the line using the point - slope form of a line.

(y - 0) = -½ (x - 5)

y = -(½) x + 5/2

or written in decimal form

y = -.5x + 2.5

Answer 3

In point slope form, the equation of the line is

y - y₁ = m(x - x₁)

x₁ = 5

y₁ = 0

Find m by knowing that the product of slopes of perpendicular lines is -1. Therefore

m = -1/2

Put it all together and get

y - 0 = (-1/2)(x - 5)

y = (-1/2)(x - 5)

Test the answer. Is the line perpendicular? (-1/2)(2) = -1 (good). Does it pass through (5,0)?

0 = (-1/2)(5 - 5) (good)

Answer 4

Think about what you know about perpendicular lines. Perpendicular lines have slopes that are inverse reciprocals. In other words, if the slope of a given line is two, the slope of a perpendicular line to it will be -1/2.

Your line is in point slope formula format. So you know the slope is 2. Therefore the initial equation of your perpendicular line will have the following format:

Y + Y1 = -1/2 (X + X1)

Now: your point is (5,0). Put those values in in place of Y1 and X1.

Y+0 = -1/2(X+5). You don’t need the zero really, but I’m putting it in there to show the substitution.

Answer 5

The given line has a slope of 2, which is the value of m in the standard equation y = mx + k.

Perpendicular lines have slopes that are the negative reciprocal of each other, so the slope of the requested line will be -1/2.

y = -x/2 + k.

Since it passes through (5,0) , plug into this equation and get

0 = -5/2 + k

So k = 5/2.

The equation is then y = -x/2 + 5/2 or (5 - x)/2

Answer 6

Hi KK R,

Recall that the slopes of perpendicular lines are negative reciprocals of each other.

Solve the given equation for y so that it will be in the slope-intercept form, y=mx + b .

y + 1 = 2x - 6

y = 2x - 7. The slope of this line is 2.

The negative reciprocal of 2 is (-1/2), which is the slope of the new line .

(5, 0) are the x₁, y₁ used in the

point- slope form for the equation of the new line.

y - 0 = (-1/2)(x -5)

y = (-1/2)x + 5/2

Regards,

Anita A.