what is the equation of the line that is perpendicular to the given line and passes through the point…

what is the equation of the line that is perpendicular to the given line and passes through the point (3,4)?\n$y = -\\frac{1}{3}x + 5$\n$y = -\\frac{1}{3}x + 3$\n$y = 3x + 2$\n$y = 3x - 5$

what is the equation of the line that is perpendicular to the given line and passes through the point (3,4)?\n$y = -\\frac{1}{3}x + 5$\n$y = -\\frac{1}{3}x + 3$\n$y = 3x + 2$\n$y = 3x - 5$

Answer

Answer:

D. ( y = 3x - 5 )

Explanation:

Step1: Find the slope of the given line

Use the slope formula ( m=\frac{y_2 - y_1}{x_2 - x_1} ). Let ( (x_1,y_1)=(-3,2) ) and ( (x_2,y_2)=(0,1) ). Then ( m=\frac{1 - 2}{0-(-3)}=\frac{-1}{3}=-\frac{1}{3} ).

Step2: Determine the slope of the perpendicular line

The slope of a line perpendicular to a line with slope ( m ) is ( m_{\perp}=-\frac{1}{m} ). Since ( m =-\frac{1}{3} ), then ( m_{\perp}=3 ).

Step3: Use the point - slope form ( y - y_1=m(x - x_1) )

We have ( m = 3 ), ( x_1 = 3 ), and ( y_1 = 4 ). Substitute into the formula: ( y - 4=3(x - 3) ).

Step4: Simplify the equation

Expand ( y - 4=3x-9 ). Add 4 to both sides: ( y=3x-9 + 4), so ( y=3x-5 ).