Question

Find the slope of the line that is ​(a) parallel and ​(b) perpendicular to the line through the pair of points.

​(-1​, -4​) and ​(0​,0​)
​(a) Select the correct choice below​ and, if​ necessary, fill in the answer box to complete your choice.

Answer 1

Answer: a) 4

b) - 1/4

Explanation:

The given line passes through the pair of points, ​(-1​, -4​) and ​(0​,0​)

Slope, m =change in value of y on the vertical axis / change in value of x on the horizontal axis

change in the value of y = y2 - y1

Change in value of x = x2 -x1

y2 = final value of y

y 1 = initial value of y

x2 = final value of x

x1 = initial value of x

Looking at the pair of points,

y2 = 0

y1 = - 4

x2 = 0

x1 = - 1

Slope = (0 - - 4)/(0 - - 1) = 4/1 = 4

a) if two lines are parallel, it means that they have the same slope. This means that the slope of the line that is parallel to the given line is 4

b) if two lines are perpendicular, it means that the slope of one line is the negative reciprocal of the other line. This means that the slope of the line that is perpendicular to the given line is - 1/4

Answer 2

a) The slope of the line is parallel to the another line m=4

b) The slope of the line is perpendicular to the another line m=
`(-1)/(4)`

Explanation:

Step1:-

Slope of a line :-

If θ is the inclination of a line 'l' then tanθ is called the slope or gradient of the line 'l'.The slope of a line is denoted by m=tanθ

The slope of a line given two points m=
`(y_(2)-y_(1)  )/(x_(2) -x_(1) )`

Parallel lines:-

Two non-vertical lines are parallel if and only if their slopes are parallel

Perpendicular lines:-

Two non-vertical lines are perpendicular to each other if and only if their slopes are negative reciprocals of each other.

`m_(2) = (-1)/(m_(1) ) \\`

Step 2:-

a)The slope of a line when given two points (-1,-4) and (0,0)

`m = (0-(-4))/(0-(-1)) =4`

Two non-vertical lines are parallel if and only if their slopes are parallel

`m_(1) = m_(2)`

Therefore the slope of the line that is parallel to the another line

`m_(1) =m_(2) =4`

Step 3:-

b) Two non-vertical lines are perpendicular to each other if and only if their slopes are negative reciprocals of each other.

`m_(2) = (-1)/(m_(1) ) \\`

`m_(2) =(-1)/(4)`

Therefore the slope of the line is perpendicular to the another line is

`m=(-1)/(4)`