Question

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

Answer 1

Answer:

A. y=3x-11

B. y=-1/3x-1

Step-by-step explanation:

I am the best at maths

Answer 2

Answer:

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

a.

∵ 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

b.

∵ 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