Question

line dr is represented by the equation y = -x - 5. determine the equation, in slope - intercept form, of the line qw that is perpendicular to line dr and passes through the point q (0, - 2).
slope of line dr: m1 = - 1
slope of line qw: m2 = 1
point - slope form of line qw: y - y1 = m(x - x1)

Explanation:

Step1: Identify slope of line DR

The equation of line DR is $y=-x - 5$, which is in slope - intercept form $y = mx + b$ where $m$ is the slope. So, $m_1=-1$.

Step2: Find slope of line QW

If two lines are perpendicular, the product of their slopes is $- 1$. Let the slope of line QW be $m_2$. Then $m_1\times m_2=-1$. Substituting $m_1 = - 1$ into the equation $(-1)\times m_2=-1$, we get $m_2 = 1$.

Step3: Use point - slope form to find equation of line QW

The point - slope form of a line is $y - y_1=m(x - x_1)$. We know that $m = m_2=1$ and the point $(x_1,y_1)=(0,-2)$. Substituting these values into the point - slope form, we have $y-(-2)=1\times(x - 0)$.

Step4: Simplify the equation

$y + 2=x$, which can be rewritten as $y=x - 2$.

Answer:

$y=x - 2$