Question

Perpendicular help i need help

Answer 1

Answer:

m₁×m₂ = -1

m₁ = 3 and m₂ = -1/3

3×-1/3 = -1

-1 = -1

Hence proved, the given two lines are perpendicular.

Step-by-step explanation:

You can prove that the two lines are perpendicular if the following condition holds true.

m₁×m₂ = -1

Where m₁ is the slope of line 1 and m₂ is slope of line 2

So first you have to find out the slope of each line.

You are given 2 equations

y = 3x + 5         eq. 1

6y + 2x = 1       eq. 2

You have to write these equations in slope-intercept form to find out their slopes.

The slope-intercept form is given by

y = mx + b

Comparing the general form with eq. 1

y = 3x + 5

We notice that the slope is m₁ = 3

Now convert the eq. 2 into slope-intercept form

6y + 2x = 1       eq. 2

6y = -2x + 1

y = (-2x + 1)/6

y = -1/3x + 1/6     eq. 2

Comparing the general form with eq. 2

y = -1/3x + 1/6

We notice that the slope is m₂ = -1/3

Now we have slopes of both lines so let us test whether they are perpendicular or not

m₁×m₂ = -1

m₁ = 3 and m₂ = -1/3

3×-1/3 = -1

-1 = -1

Hence proved, the given two lines are perpendicular.