what is the slope of a line that is perpendicular to the line y = -\\frac{1}{4}x - 1?

Explanation:

Step1: Identify the slope of given line

The given line is $y =-\frac{1}{4}x - 1$, and its slope $m_1=-\frac{1}{4}$.

Step2: Use the perpendicular - slope formula

If two lines are perpendicular, the product of their slopes $m_1$ and $m_2$ is - 1, i.e., $m_1\times m_2=-1$. Substitute $m_1 =-\frac{1}{4}$ into the formula: $-\frac{1}{4}\times m_2=-1$.

Step3: Solve for $m_2$

Multiply both sides of the equation $-\frac{1}{4}\times m_2=-1$ by - 4 to get $m_2 = 4$.

Answer:

4