Question

Write the equation of the line perpendicular to y=3x-1 that passes through the point (3,-4)

explanation or step by step pls

thanku

Answer 1

`y=-(1)/(3)x - 3`

Explanation:

Hi there!

We want to write an equation of the line that is perpendicular to y=3x-1 and passes through (3, -4)

Perpendicular lines have slopes that multiply to get the value of negative one.

Let's first figure out the slope of y=3x-1

The line is written in slope-intercept form, which is y=mx+b, where m is the slope and b is the y intercept

3 is in the place of where m is, so 3 is the slope of y=3x-1

Now let's find the slope of the line perpendicular to it.

We can use a formula like this:

`m_1 * m_2= -1`

If 3 is
`m_1`, then:

`3*m_2=-1`

Divide both sides by 3

`m_2=-(1)/(3)`

So the slope of the perpendicular line is -1/3

We can write this equation in slope-intercept form. So far, we know that the equation of the line is:

y=
`-(1)/(3)x + b`

So let's find b

Remember that we are given that the line passes through the point (3, -4). That means that point is a solution to the equation that we're trying to find. Therefore, the values of that point should create a true statement when plugged into the equation.

So we can substitute 3 as x and -4 as y to help solve for b.

-4=
`-(1)/(3)(3)+b`

Multiply

-4=
`-(3)/(3)` + b

Simplify

-4 = -1 + b

Add 1 to both sides to isolate b

-3 = b

Substitute -3 as b in the equation

`y=-(1)/(3)x - 3`

Hope this helps!