Question

line wn is perpendicular to line tr. line tr is represented by the equation y = -x + 2. line wn passes through the point w (4, 11). determine the equation of line wn in slope - intercept form.
slope of line tr: m1
slope of line wn: m2
point - slope form of line wn: y - y1 = m(x - x1)

Explanation:

Step1: Find slope of line TR

The equation of line TR is not given directly from the graph, but we know the relationship between slopes of perpendicular lines. The equation of line WN is found using the fact that if two lines are perpendicular, the product of their slopes is - 1. The equation of line WN is related to the line \(y=-x + 2\). The slope of the line \(y=-x + 2\) is \(m=-1\). Let the slope of line TR be \(m_1\) and the slope of line WN be \(m_2\). For perpendicular lines \(m_1\times m_2=-1\). Since the line WN is perpendicular to the line with equation \(y=-x + 2\), the slope of line WN, \(m_2 = 1\) (because \((-1)\times1=-1\)).

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

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 of the line. We know that line WN passes through the point \(W(4,11)\) and has a slope \(m = 1\). Substitute \(x_1 = 4\), \(y_1=11\) and \(m = 1\) into the point - slope form:
\[y-11=1\times(x - 4)\]
\[y-11=x - 4\]
\[y=x+7\]

Answer:

The equation of line WN in slope - intercept form is \(y=x + 7\)