SOLUTION: Find the slope of each line and determine if the lines are parallel, perpendicular, or neither.
54) The line y - 4x = -1 and the line x + 4y =12 .
Algebra.Com
Question 81947: Find the slope of each line and determine if the lines are parallel, perpendicular, or neither.
54) The line y - 4x = -1 and the line x + 4y =12 .
Answer by bucky(2189) (Show Source): You can put this solution on YOUR website!
Given:
.
the lines y - 4x = -1 and x + 4y =12
.
find whether the lines are parallel, perpendicular, or neither.
.
To do this problem you need to know the slope of each line. If the slopes are identical
the lines are either parallel or co-linear (one on top of the other). If the slopes are
negative inverses, the lines are perpendicular. Examples of negative inverses are:
.
6 and -1/6
.
-3 and +1/3
.
A way you can find the slope is to convert the equation for each line to the slope-intercept
form of:
.
y = mx + b
.
If you get the equation of the line in this form, m, which is the multiplier of the x term,
is the slope and b is the point on the y-axis where the line intersects.
.
Let's rearrange the equation of the first line into the slope-intercept form.
.
y - 4x = -1
.
Get rid of the -4x on the left side by adding 4x to both sides. When you add 4x to both
sides the equation becomes:
.
y = 4x -1
.
Note that this is in the slope intercept form. The slope of this line is +4 (which is the
multiplier of the x) and the line crosses the y-axis at -1.
.
Let's now work the second equation into the slope intercept form.
.
x + 4y = 12
.
get rid of the x on the left side by subtracting x from both sides. This
subtraction changes
the equation to:
.
4y = -x + 12
.
Divide both sides by 4 to solve for y:
.
y = -x/4 + 12/4
.
and this simplifies to:
.
y = (-1/4)x + 3
.
In this equation the slope is -1/4 and the line crosses the y-axis at +3.
.
Compare the two slopes. One line has a slope of +4 and the other a slope of -1/4.
The slopes are negative inverses and, therefore, the two lines are perpendicular.
.
Cheers!!!
RELATED QUESTIONS
1. draw the graph of each line using its y-intercept and its slope:
4x+3y=9
2. (answered by checkley71)
give the slope of each line and then determine whether the two lines are parallel,... (answered by Alan3354)
Give the slope of each line and then determine whether the two lines are parallel, (answered by Fombitz,MathTherapy)
The equations of three lines are given below:
Line 1: 4y = 3x + 5
Line 2: y = 3/4x... (answered by ikleyn)
find the slope of each line.
y = 2x -3
2y = -x + 4
In each pair of equations give the... (answered by ewatrrr)
Give the slope of each line AND then determine whether the two lines are parallel,... (answered by richwmiller,solver91311)
Give the slope of each line AND then determine whether the two lines are parallel,... (answered by dfrazzetto)
what is the slope of each line and then determine whether the two lines are parallel,... (answered by stanbon)
Give the slope of each line and then determine whether the two lines are parallel,... (answered by solver91311)