Lines and relative positionwhat is the relative position of the lines? 4x+5y=198 5x-4y=145
To verify if the given lines are parallel, perpendicular or neither, we'll have to put them first, in the point slope form:
y = mx + n
We'll start with the first equation:
We'll keep 5y to the left side and we'll move 4x to the right side:
5y = -4x + 198
We'll divide by 5:
y = -4x/5 + 198/5
Now, we'll put the 2nd equation in the point slope form:
We'll keep -4y to the left side:
-4y = -5x + 145
We'll divide by -4:
y = 5x/4 - 145/4
We know that 2 lines are parallel if their slopes are equal.
The slope of the 1st line is m1 = -4/5 and the slope of the 2nd line is m2 = 5/4. The values are not equal so the lines are not parallel.
We know that 2 lines are perpendicular if the product of their slopes is -1.
m1*m2 = (-4/5)*(5/4)
We'll simplify and we'll get:
m1*m2 = -1
Since the product of their slopes is -1, the lines are perpendicular.