|
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!!!
|
|
|
| |
