the equation for line v can be written as ( y = -\frac{9}{7}x - 5 ). line w, which is perpendicular to line…

the equation for line v can be written as ( y = -\frac{9}{7}x - 5 ). line w, which is perpendicular to line v, includes the point ( (9, 6) ). what is the equation of line w? write the equation in slope - intercept form. write the numbers in the equation as simplified proper fractions, improper fractions, or integers.

the equation for line v can be written as ( y = -\frac{9}{7}x - 5 ). line w, which is perpendicular to line v, includes the point ( (9, 6) ). what is the equation of line w? write the equation in slope - intercept form. write the numbers in the equation as simplified proper fractions, improper fractions, or integers.

Answer

Explanation:

Step1: Find the slope of line (w)

If two lines are perpendicular, the product of their slopes is (- 1). Let the slope of line (v) be (m_v=-\frac{9}{7}), and the slope of line (w) be (m_w). Then (m_v\times m_w=-1). So (-\frac{9}{7}\times m_w=-1), and (m_w = \frac{7}{9}).

Step2: Use the point - slope form (y - y_1=m(x - x_1))

We know that (m=\frac{7}{9}) and the point ((x_1,y_1)=(9,6)). Substitute into the point - slope form: (y - 6=\frac{7}{9}(x - 9)).

Step3: Convert to slope - intercept form (y=mx + b)

Expand the right - hand side: (y-6=\frac{7}{9}x-7). Add (6) to both sides: (y=\frac{7}{9}x-7 + 6).

Answer:

(y=\frac{7}{9}x-1)