Answer:
First part
Slope of a parallel line:
[tex]-4[/tex]
Slope of a perpendicular line:
[tex]\dfrac{1}{4}[/tex]
Second part
Lines are parallel (same slope)
Step-by-step explanation:
The equation of the line is
y = -4x -3
This is the slope intercept form of a line more generally
y = mx + b
where m is the slope, b is the y-intercept
The slope of any line parallel to y = mx + b will have the same slope(different y-intercept)
So a line parallel to y = -4x - 3 will have slope = -4
A line perpendicular to y = mx + b will have a slope that is the negative reciprocal of m
Therefore the perpendicular line will have slope -1/m
A line perpendicular to y = -4x - 3 will have slope
[tex]-\dfrac{1}{-4} = \dfrac{1}{4}[/tex]
For the second part, the lines are parallel since they have the same slope
