Question

Find the equation of parallel line and perpendicular line .

Answer 1

Part 1)

The slope-intercept form of the line equation

`y = mx+b`

where m is the slope and b is the y-intercept

Given the equation

`y = 3x-4`

comparing with the slope-intercept form of the line equation y = 3x-4

Thus, the slope of the line: m = 3

We know that the parallel lines have the same slopes.

Thus, the slope of the paralellel line is also: 3

substituting the slope m = 3 and the point (5, -3) in the slope-intercept form

`y = mx+b`

-3 = 3(5) + b

-3 = 15 + b

b = -3-15

b = -18

Therefore, the value of y-intercept b = -18

now substituting the slope m = 3 and the y-intercept b = -18 in the slope-intercept form

`y = mx+b`

y = 3x + (-18)

y = 3x - 18

Therefore, the equation of line parallel to the given line
`y = 3x-4` will be:

`y = 3x - 18`

Part 2)

The slope-intercept form of the line equation

`y = mx+b`

where m is the slope and b is the y-intercept

Given the equation

`y = 3x-4`

comparing with the slope-intercept form of the line equation y = 3x-4

Thus, the slope of the line: m = 3

We know that a line perpendicular to another line contains a slope that is the negative reciprocal of the slope of the other line, such as:

slope = m = 3

Thus, the slope of the the new perpendicular line = – 1/m = -1/3 = -1/3

substituting m = -1/3 and the point (5, -3) in the slope-intercept form

`y = mx+b`

`-3\:=\:-(1)/(3)\left(5\right)+b`

`-(5)/(3)+b=-3`

`b=-(4)/(3)`

now substituting the slope m = -1/3 and the y-intercept b = -4/3 in the slope-intercept form

`y = mx+b`

`y=\:-(1)/(3)x+\left(-(4)/(3)\right)`

`y=\:-(1)/(3)x-(4)/(3)`

Therefore, the equation of the line perpendicular to the given line will be:

• 
  `y=\:-(1)/(3)x-(4)/(3)`