Lines and relative positionwhat is the relative position of the lines? 4x+5y=198 5x-4y=145

giorgiana1976 | College Teacher | (Level 3) Valedictorian

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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

4x+5y=198

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:

5x-4y=145

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.