Find the slope of the line that is
a) parallel and
b) perpendicular to the given line.
1. x=-8
2. y=10
there are many lines both parallel and perpendicular to any line
x=2 x=0 x=9 are all parallel to x = -8
y=-10000 y=.0003 y=4 are all parallel to y=10
400 miles-25
To find the slope of a line, we need to check the equation of the line in slope-intercept form, which is y = mx + b, where m represents the slope.
1. For the equation x = -8, this line is vertical parallel to the y-axis. A vertical line has an undefined slope since it does not rise or fall. Therefore, a parallel line to x = -8 would also have an undefined slope.
2. For the equation y = 10, this line is horizontal parallel to the x-axis. A horizontal line has a slope of 0 since it does not rise or fall. Therefore, a parallel line to y = 10 would also have a slope of 0.
For the perpendicular line, we need to find the negative reciprocal of the original line's slope.
1. Since x = -8 has no slope, it does not have a perpendicular line.
2. The slope of the line y = 10 is 0. To find the negative reciprocal, we flip the fraction and change its sign. Since 0 can be written as 0/1, its negative reciprocal is -1/0. However, this is undefined since division by zero is not defined. Thus, line y = 10 does not have a perpendicular line either.