Question

question
find the slope of a line perpendicular to the line whose equation is ( x + y = -6 ). fully simplify your ans

Explanation:

Step1: Find slope of given line

Rewrite \(x + y=-6\) in slope - intercept form \(y = mx + b\) (where \(m\) is the slope).
Subtract \(x\) from both sides: \(y=-x - 6\). The slope of the line \(y=-x - 6\) is \(m_1=-1\).

Step2: Find slope of perpendicular line

If two lines are perpendicular, the product of their slopes \(m_1\) and \(m_2\) is \(- 1\), i.e., \(m_1\times m_2=-1\).
We know \(m_1 = - 1\), so \(-1\times m_2=-1\). Solving for \(m_2\), we divide both sides by \(-1\): \(m_2 = 1\).

Answer:

The slope of the line perpendicular to the line \(x + y=-6\) is \(1\).