Question

1) Write an equation of the line perpendicular to: y = 3x - 9 with a y-intercept of 4.

Answer 1

The given equation is

`y=3x-9`

The new line is perpendicular to the given equation, which means we have to use the following formula.

`m\cdot m_1=-1`

Where the slope of the given line is 3 (the coefficient of x).

`m\cdot3=-1`

We solve for m.

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

So, the slope of the new perpendicular line is -1/3.

According to the problem, the y-intercept of the new perpendicular line is 4. Now, we use the slope-intercept form to write the equation.

`\begin{gathered} y=mx+b \\ y=-(1)/(3)x+4 \end{gathered}`

Therefore, the equation of the new line is

`y=-(1)/(3)x+4`