Question

line ds is perpendicular to line tp. line tp is represented by the equation y = x - 2. line ds passes through the point d(2,0). determine the equation of line ds in slope - intercept form. y =
slope of line tp | slope of line ds | point - slope form of line ds
m1 | m2 | y - y1 = m(x - x1)

Explanation:

Step1: Find slope of line TP

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

Step2: Find slope of line DS

If two lines are perpendicular, the product of their slopes is - 1. Let the slope of line DS be $m_2$. Then $m_1\times m_2=-1$. Since $m_1 = 1$, we have $1\times m_2=-1$, so $m_2=-1$.

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

The point - slope form of a line is $y - y_1=m(x - x_1)$. Line DS passes through the point $D(2,0)$ and has a slope $m=-1$. Substituting $x_1 = 2$, $y_1 = 0$ and $m=-1$ into the point - slope form, we get $y-0=-1(x - 2)$.

Step4: Convert to slope - intercept form

Simplify the equation $y-0=-1(x - 2)$:
$y=-x + 2$.

Answer:

$y=-x + 2$