2 lines are given by kx+6y-5=0 and 3x+2y+4=0 if they are parrallel what is the value of k
since they are parallel,
k/6 = 3/2
2k = 18
k = 9
To determine if two lines are parallel, we need to compare their slopes.
The given lines are in the form of `ax + by + c = 0`. We can rewrite them in slope-intercept form `y = mx + b` by isolating the `y` variable.
For the first line, `kx + 6y - 5 = 0`, we rearrange it as:
6y = -kx + 5
y = (-k/6)x + 5/6
So, the slope of the first line is -k/6.
For the second line, `3x + 2y + 4 = 0`, we rearrange it as:
2y = -3x - 4
y = (-3/2)x - 2
So, the slope of the second line is -3/2.
If two lines are parallel, their slopes must be equal.
Therefore, we can equate -k/6 and -3/2 to find the value of k:
-k/6 = -3/2
To solve for k, we can cross-multiply:
2(-k) = -3(6)
-2k = -18
k = 9
Thus, the value of k is 9.
k=9
when you solve for y for the second equation, you get:
y=-3/2x-2
therefore, the slope has to be -3/2 to be parallel
when you solve for y in the first equation, you get:
y=-k/6x+5/6
so to have the same -1.5 slope, you need k to be 9