Question

Determine if the equations are perpendicular 3/125x-y/5=1 25/3x-y+1=0

Answer 1

Answer: they are not perpendicular

Step-by-step explanation:

For the two equation to be perpendicular, the product of their slope must equals - 1.

We must made the equation to look like this

y = mx + c

Where m is the slope.

Now we shall find the slope of the individual equation as follows:

3/125x - y/5 = 1

Multiply through by 5 to make the coefficient of y to be 1, we have:

5(3/125x) - 5(y/5) = 5(1)

3/25x - y = 5

Now, Make y the subject, we have:

3/25x - y = 5

3/25x - 5 = y

Re-arranging, we have:

y = 3/25x - 5

Therefore the slope(m1) = 3/25

Now let us find the slope for the second equation

25/3x - y + 1= 0

Make y the subject, we have:

25/3x - y + 1= 0

25/3x + 1 = y

Re-arranging, we have:

y = 25/3x + 1

The slope(M2) = 25/3

Let us find the product of m1 and m2:

m1 x m2 = 3/25 x 25/3 = 1

Since the product of the slopes did not result to - 1, the equation are not perpendicular.