Question

line vw is perpendicular to line ze. line ze is represented by the equation y = x - 6. line vw passes through the point v(-2, -6). determine the equation of line vw in slope - intercept form.
slope of line ze: m1 = 1
slope of line vw: m2=-1
point - slope form of line vw: y - y1 = m(x - x1), y-(-6)=-(x - (-2))

Explanation:

Step1: Find slope of line ZE

The equation of line ZE is $y = x - 6$, which is in slope - intercept form $y=mx + b$ where $m$ is the slope. So, the slope of line ZE, $m_1=1$.

Step2: Find slope of line VW

If two lines are perpendicular, the product of their slopes is $- 1$. Let the slope of line VW be $m_2$. Since $m_1\times m_2=-1$ and $m_1 = 1$, then $1\times m_2=-1$, so $m_2=-1$.

Step3: Write point - slope form of line VW

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 VW passes through the point $V(-2,-6)$ and has a slope $m=-1$. Substituting $x_1=-2$, $y_1 = - 6$ and $m=-1$ into the point - slope form, we get $y-(-6)=-1(x - (-2))$, which simplifies to $y + 6=-(x + 2)$.

Step4: Convert to slope - intercept form

Expand the right - hand side: $y+6=-x - 2$. Then subtract 6 from both sides to get $y=-x-8$.

Answer:

$y=-x - 8$