line v has an equation of ( y = -\frac{10}{9}x - 3 ). perpendicular to line v is line w, which passes…
line v has an equation of ( y = -\frac{10}{9}x - 3 ). perpendicular to line v is line w, which passes through the point ( (2, 3) ). 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 )
The slope of line ( v ) is ( m_v=-\frac{10}{9} ). If two lines are perpendicular, then ( m_v\times m_w=- 1 ). Let the slope of line ( w ) be ( m_w ), so ( -\frac{10}{9}\times m_w=-1 ). Solving for ( m_w ), we get ( m_w=\frac{9}{10} ).
Step2: Use the point - slope form to find the equation of line ( w )
The point - slope form is ( y - y_1=m_w(x - x_1) ), where ( (x_1,y_1)=(2,3) ) and ( m_w=\frac{9}{10} ). Substitute the values: ( y - 3=\frac{9}{10}(x - 2) ).
Step3: Convert to slope - intercept form
Expand the right side: ( y-3=\frac{9}{10}x-\frac{9}{5} ). Add ( 3 ) to both sides: ( y=\frac{9}{10}x-\frac{9}{5}+3 ). Since ( 3=\frac{15}{5} ), then ( y=\frac{9}{10}x+\frac{-9 + 15}{5} ). Simplify to get ( y=\frac{9}{10}x+\frac{6}{5} ).
Answer:
( y=\frac{9}{10}x+\frac{6}{5} )