Lines 2x-8y=- 24 and x-4y=4 are parallel. Line 4x+y=- 2 is perpendicular to lines 2x-8y=- 24 and x-4y=4.
Practice makes perfect
Two lines are parallel if their slopes are identical.
To tell if two lines are perpendicular, we check if their slopes are opposite reciprocals. Let's tackle these questions one at a time.
Are They Parallel?
To start, let's write each equation in slope-intercept form, highlighting their slopes.
Line
Given Equation
Slope-Intercept Form
Slope
a
2x-8y=- 24
y=1/4x+3
m_1=1/4
b
4x+y=- 2
y=- 4x-2
m_2=- 4
c
x-4y=4
y=1/4x-1
m_3=1/4
Now that we have identified the slope of each line, we can see that a and c have the same slope, so they are parallel.
Are They Perpendicular?
For lines with different slopes, we can conclude that they are not parallel. To determine whether or not they are perpendicular, we calculate the product of their slopes. Any two slopes whose product equals - 1 are opposite reciprocals, and are therefore perpendicular.
Let's start with checking lines a and b.
