write an equation for line l in point - slope form and slope - intercept form. l is perpendicular to y = 3x.

Explanation:

Step1: Find the slope of line L

The slope of the line $y = 3x$ is $m_1=3$. If two lines are perpendicular, the product of their slopes is - 1. Let the slope of line L be $m_2$. Then $m_1\times m_2=-1$, so $3m_2=-1$, and $m_2 =-\frac{1}{3}$.

Step2: Write the point - slope form

The point - slope form of a line is $y - y_1=m(x - x_1)$, where $(x_1,y_1)$ is a point on the line and $m$ is the slope. The line L passes through the point $(-1,-3)$, so substituting $x_1=-1,y_1 = - 3$ and $m=-\frac{1}{3}$ into the point - slope form, we get $y+3=-\frac{1}{3}(x + 1)$.

Step3: Write the slope - intercept form

Starting from the point - slope form $y+3=-\frac{1}{3}(x + 1)$, we expand the right - hand side: $y+3=-\frac{1}{3}x-\frac{1}{3}$. Then we solve for $y$ by subtracting 3 from both sides: $y=-\frac{1}{3}x-\frac{1}{3}-3=-\frac{1}{3}x-\frac{1 + 9}{3}=-\frac{1}{3}x-\frac{10}{3}$.

Answer:

Point - slope form: $y + 3=-\frac{1}{3}(x + 1)$ Slope - intercept form: $y=-\frac{1}{3}x-\frac{10}{3}$