Question

line qr is represented by the equation y = -x - 7. line dg is perpendicular to line qr. the coordinates of point d are (-1, -12). determine the equation of line dg in slope - intercept form.
slope of line qr m1
slope of line dg m2
point - slope form of line dg y - y1 = m(x - x1)

Explanation:

Step1: Find slope of line QR

The equation of line QR is $y=-x - 7$, which is in slope - intercept form $y = mx + b$ where $m$ is the slope. So, $m_1=-1$.

Step2: Find slope of line DG

If two lines are perpendicular, the product of their slopes is $- 1$. Let the slope of line DG 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 point - slope form

The point - slope form of a line is $y - y_1=m(x - x_1)$. We know a point $D(-1,-12)$ on line DG and $m_2 = 1$. Substituting $x_1=-1$, $y_1=-12$ and $m = 1$ into the point - slope form, we get $y-(-12)=1\times(x - (-1))$, which simplifies to $y + 12=x + 1$, or $y=x - 11$.

Answer:

$y=x - 11$