Question

line wg is perpendicular to line pq. line pq is represented by the equation y = - 4x + 8. line wg passes through the point w(-4, -1). determine the equation of line wg in slope - intercept form. y = 4 1/4 x
slope of line pq
m1
slope of line wg
m2
point - slope form of line wg
y - y1 = m(x - x1)

Explanation:

Step1: Recall slope - perpendicular relationship

If two lines are perpendicular, the product of their slopes is - 1. Given the equation of line PQ is $y = \frac{1}{4}x$, its slope $m_1=\frac{1}{4}$. Let the slope of line WG be $m_2$. Then $m_1\times m_2=-1$.

Step2: Calculate the slope of line WG

Substitute $m_1 = \frac{1}{4}$ into $m_1\times m_2=-1$. We get $\frac{1}{4}\times m_2=-1$, so $m_2=-4$.

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

The point - slope form of a line is $y - y_1=m(x - x_1)$, where $(x_1,y_1)=(-4,-1)$ and $m = m_2=-4$. Substitute these values into the formula: $y-(-1)=-4(x - (-4))$.

Step4: Simplify the equation

$y + 1=-4(x + 4)$. Expand the right - hand side: $y+1=-4x-16$. Then, rewrite it in slope - intercept form $y=-4x-17$.

Answer:

The equation of line WG in slope - intercept form is $y=-4x - 17$