what is the equation, in point - slope form, of the line that is perpendicular to the given line and passes…

Explanation:

Step1: Find slope of given line

Use two - point formula $m=\frac{y_2 - y_1}{x_2 - x_1}$ with points $(-1,1)$ and $(0, - 3)$. So $m_1=\frac{-3 - 1}{0+1}=-4$.

Step2: Find slope of perpendicular line

If two lines are perpendicular, the product of their slopes is $- 1$. Let the slope of the perpendicular line be $m_2$. Then $m_1\times m_2=-1$. Since $m_1 = - 4$, we have $-4\times m_2=-1$, so $m_2=\frac{1}{4}$.

Step3: Write point - slope form equation

The point - slope form of a line is $y - y_1=m(x - x_1)$. The line passes through $(-4,-3)$ and has slope $m=\frac{1}{4}$. Substituting $x_1=-4$, $y_1 = - 3$ and $m=\frac{1}{4}$ into the formula, we get $y+3=\frac{1}{4}(x + 4)$.

Answer:

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