line p has an equation of ( y=\frac{5}{3}x - 4 ). line q includes the point ( (-10,-3) ) and is…

line p has an equation of ( y=\frac{5}{3}x - 4 ). line q includes the point ( (-10,-3) ) and is perpendicular to line p. what is the equation of line q? write the equation in slope - intercept form. write the numbers in the equation as simplified proper fractions, improper fractions, or integers.

line p has an equation of ( y=\frac{5}{3}x - 4 ). line q includes the point ( (-10,-3) ) and is perpendicular to line p. what is the equation of line q? 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 ( q )

The slope of line ( p ) is ( m_p=\frac{5}{3} ). If two lines are perpendicular, the product of their slopes is ( - 1), i.e., (m_p\times m_q=-1). Let the slope of line ( q ) be ( m_q ), then (\frac{5}{3}\times m_q=-1), so (m_q =-\frac{3}{5}).

Step2: Use the point - slope form to find the equation of line ( q )

The point - slope form of a line is (y - y_1=m(x - x_1)), where ((x_1,y_1)=(-10,-3)) and (m =-\frac{3}{5}). Substitute the values into the formula: (y-(-3)=-\frac{3}{5}(x - (-10))). Simplify: (y + 3=-\frac{3}{5}(x + 10)).

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

Expand the right side: (y+3=-\frac{3}{5}x-6). Subtract 3 from both sides: (y=-\frac{3}{5}x-6 - 3). So (y=-\frac{3}{5}x-9).

Answer:

(y =-\frac{3}{5}x-9)