Mathematics, 04.11.2020 08:50 rebekahhenton

Write an equation of the line that passes through the given point and is (a) parallel and (b) perpendicular to the given line.

Write an equation of the line that passes through the given point and is (a) parallel and (b) perpe

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Answer from: llamasking

The equation of the line parallel to the line is y = -4x + 10

The equation of the line perpendicular to the line is y = 1/4x +3/2

Using the point (1, 6) and (2, 2) on the line to get the slope:

Slope = 2-6/2-1

Slope = -4/1

Slope = -4

The equation in point slope form is expressed as y-y0 = m(x-x0)

Substitute a point and te given slope for the equation parallel to the line

y - 2 = -4(x-2)

y - 2 = -4x + 8

y+4x = 10

Hence the equation of the line parallel to the line is y = -4x + 10

For the line perpendicular, the required slope is 1/4

Substitute a point and te given slope for the equation parallel to the line

y - 2 = 1/4(x-2)

4(y - 2) = x - 2

4y - 8 =x -2

4y = x + 6

y = 1/4x + 3/2

Hence the line perpendicular to the line is y = 1/4x + 3/2

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Answer from: joelpimentel

a. The equation of the parallel line to the given line is y = -4x + 19

b. The equation of the perpendicular line to the given line is y = $\frac{1}{4}$ x + 2

Step-by-step explanation:

Parallel lines have the same slopes

If the slope of one of them is m, then the slope of the other is m

The product of the slopes of the perpendicular lines is -1

If the slope of one of them is m, then the slope of the other is $-\frac{1}{m}$ To find the slope of a perpendicular line to a given line reciprocal the slope of the given line and change its sign

The rule of the slope is m = $\frac{y2-y1}{x2-x1}$ , where

(x1, y1) and (x2, y2) are the points on the line

The form of the equation of a line is y = m x + b, where

m is the slope b is the y-intercept

Let us solve the question

∵ The given line passes through points (1, 6) and (2, 2)

∴ x1 = 1 and y1 = 6

∴ x2 = 2 and y2 = 2

→ Substitute them in the rule of the slope to find it

∵ m = $\frac{2-6}{2-1}=\frac{-4}{1}=-4$

∴ The slope of the given line is -4

∵ The line is parallel to the given line

∴ Their slopes are equal

∵ The slope of the given line = -4

∴ The slope of the parallel line = -4

→ Substitute its value in the form of the equation above

∴ y = -4x + b

→ To find b substitute x and y in the equation by the coordinates

of any point on the line

∵ The parallel line passes through the point (4, 3)

∴ x = 4 and y = 3

∵ 3 = -4(4) + b

∴ 3 = -16 + b

→ Add 16 to both sides

∴ 3 + 16 = -16 + 16 + b

∴ 19 = b

→ Substitute it in the equation

∴ y = -4x + 19

The equation of the parallel line to the given line is y = -4x + 19

∵ The line is perpendicular to the given line

∴ The product of their slopes is -1

→ Reciprocal the slope of the given line and change its sign

∵ The slope of the given line = -4

∴ The slope of the perpendicular line = $\frac{1}{4}$

→ Substitute its value in the form of the equation above

∴ y = $\frac{1}{4}$ x + b

→ To find b substitute x and y in the equation by the coordinates

of any point on the line

∵ The perpendicular line passes through the point (4, 3)

∴ x = 4 and y = 3

∵ 3 = $\frac{1}{4}$ (4) + b

∴ 3 = 1 + b

→ Subtract 1 from both sides

∴ 3 - 1 = 1 - 1 + b

∴ 2 = b

→ Substitute it in the equation

∴ y = $\frac{1}{4}$ x + 2

The equation of the perpendicular line to the given line is y = $\frac{1}{4}$ x + 2

Answer from: Quest

452,489 to the nearest thousand is 452,000

Answer from: Quest

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