Write an equation of a line perpendicular to line CD in slope-intercept form that passes through the point (−1, 6).

Line CD is shown. C is at 1, 1. D is at 3, 5.

y = −0.5x − 5.5
y = −0.5x + 5.5
y = 2x + 13
y = 2x − 13

Answers

Answer 1

Answer:

its b

Step-by-step explanation:

i took the test

Answer 2

y = - 0.5x + 5.5 is the equation of a line perpendicular to line CD in slope-intercept form that passes through the point (−1, 6).

What is the slope-intercept form of a straight line?

The slope-intercept form of a straight line is y = mx + c.

Here, x and y are coordinates, m is the slope and c is the y-intercept of the line.

Given, two points are C(1, 1) and (3, 5).

Therefore, equation of the line CD is:

[tex]\frac{x - x_{1} }{y-y_{1} }[/tex] = [tex]\frac{x_{1}-x_{2}}{y_{1}-y_{2}}[/tex]

⇒ [tex]\frac{x - 1}{y-1}[/tex] = [tex]\frac{1-3}{1-5}}[/tex]

⇒  [tex]\frac{x - 1}{y-1}[/tex] = [tex]\frac{-2}{-4}}[/tex]

⇒2(x - 1) = (y - 1)

⇒ y = 2x - 1

Let, line AB is perpendicular to the line CD and passes through the point (-1, 6).

Therefore, slope of the line CD is = 2.

We know, slope of CD × slope of AB = -1

Therefore, slope of AB = -1 / slope of CD = [tex]-\frac{1}{2}[/tex].

Now, line AB has a slope of [tex]-\frac{1}{2}[/tex] and passes through the point (-1, 6).

Therefore, equation of the line AB is:

(y - y₁) = m(x - x₁)

⇒ [y - (6)] = [tex]-\frac{1}{2}[/tex][x - (- 1)]

⇒ 2(y - 6) = (-x - 1)

⇒ 2y - 12 + x + 1 = 0

⇒ x + 2y = 11

⇒ y = - 0.5x + 5.5

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Answers

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hope this helps

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Answers

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Answers

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