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.

$m=-\frac{1}{3}$

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.

$\begin{gathered} y=mx+b \\ y=-\frac{1}{3}x+4 \end{gathered}$

Therefore, the equation of the new line is

$y=-\frac{1}{3}x+4$