Question

line rl is represented by the equation y = -x - 2. determine the equation, in slope - intercept form, of the line vt that is perpendicular to line rl and passes through the point v (13, 18). y =

Explanation:

Step1: Find the slope of line RL

The equation of line RL is $y=-x - 2$, which is in the form $y = mx + b$ where $m$ is the slope. So the slope of line RL, $m_1=-1$.

Step2: Find the slope of line VT

If two lines are perpendicular, the product of their slopes is - 1. Let the slope of line VT 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: Use the point - slope form to find the equation of line VT

The point - slope form of a line is $y - y_1=m(x - x_1)$, where $(x_1,y_1)=(13,18)$ and $m = m_2=1$. Substitute these values: $y - 18=1\times(x - 13)$.

Step4: Convert to slope - intercept form

Expand the right - hand side: $y-18=x - 13$. Add 18 to both sides to get $y=x + 5$.

Answer:

$y=x + 5$