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.

m1: slope of line pq

m2: slope of line wg

y - y1 = m(x - x1): point - slope form of line wg

Explanation:

Step1: Find slope of line WG

If two lines are perpendicular, the product of their slopes is - 1. The slope of line PQ is related to the slope of line WG by $m_1\times m_2=-1$. The equation of a line is given by $y = mx + b$, where $m$ is the slope. For the line $y=-4x + 8$, the slope of the line perpendicular to it (slope of line WG, $m_2$) is $\frac{1}{4}$ since $-4\times m_2=-1$, so $m_2=\frac{1}{4}$.

Step2: Use point - slope form to find equation of line WG

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. We know that the line WG passes through the point $W(-4,-1)$ and has a slope $m=\frac{1}{4}$. Substituting $x_1=-4$, $y_1 = - 1$ and $m=\frac{1}{4}$ into the point - slope form, we get $y-(-1)=\frac{1}{4}(x - (-4))$.

Step3: Simplify the equation

$y + 1=\frac{1}{4}(x + 4)$
$y+1=\frac{1}{4}x + 1$
$y=\frac{1}{4}x$

Answer:

The slope of line WG ($m_2$) is $\frac{1}{4}$ and the equation of line WG in slope - intercept form is $y=\frac{1}{4}x$