Answer:
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=![\frac{-1}{4}](https://tex.z-dn.net/?f=%5Cfrac%7B-1%7D%7B4%7D)
Step-by-step explanation:
Step1:-
<u>Slope of a line</u><u> :-</u>
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=![\frac{y_{2}-y_{1} }{x_{2} -x_{1} }](https://tex.z-dn.net/?f=%5Cfrac%7By_%7B2%7D-y_%7B1%7D%20%20%7D%7Bx_%7B2%7D%20-x_%7B1%7D%20%7D)
<u>Parallel lines:-</u>
<u>Two </u>non-vertical lines are parallel if and only if their slopes are parallel
<u>Perpendicular lines:-</u>
<u>Two </u>non-vertical lines are perpendicular to each other if and only if their slopes are negative reciprocals of each other.
<u>Step 2</u>:-
a)The slope of a line when given two points (-1,-4) and (0,0)
![m = \frac{0-(-4)}{0-(-1)} =4](https://tex.z-dn.net/?f=m%20%3D%20%5Cfrac%7B0-%28-4%29%7D%7B0-%28-1%29%7D%20%3D4)
<u>Two </u>non-vertical lines are parallel if and only if their slopes are parallel
![m_{1} = m_{2}](https://tex.z-dn.net/?f=m_%7B1%7D%20%3D%20m_%7B2%7D)
Therefore the slope of the line that is parallel to the another line
![m_{1} =m_{2} =4](https://tex.z-dn.net/?f=m_%7B1%7D%20%3Dm_%7B2%7D%20%3D4)
<u>Step 3</u>:-
b) <u>Two </u>non-vertical lines are perpendicular to each other if and only if their slopes are negative reciprocals of each other.
![m_{2} = \frac{-1}{m_{1} } \\](https://tex.z-dn.net/?f=m_%7B2%7D%20%3D%20%5Cfrac%7B-1%7D%7Bm_%7B1%7D%20%7D%20%5C%5C)
![m_{2} =\frac{-1}{4}](https://tex.z-dn.net/?f=m_%7B2%7D%20%3D%5Cfrac%7B-1%7D%7B4%7D)
Therefore the slope of the line is perpendicular to the another line is
![m=\frac{-1}{4}](https://tex.z-dn.net/?f=m%3D%5Cfrac%7B-1%7D%7B4%7D)