Question

What is the equation of a line that passes through the point (8, 1) and is perpendicular to the line whose equation is y=−23x+5y=−23x+5 ? enter your answer in the box?

Answer 1

Answer:

$y=\frac{3}{2}x-11$

Step-by-step explanation:

We have been given an equation $y=-\frac{2}{3}x+5$. We are asked to find the equation of line perpendicular to our given equation and passes through point (8,1).

We know that the slope of a perpendicular line to a given line is negative reciprocal of the slope of given line. So the slope of perpendicular line to the line $y=-\frac{2}{3}x+5$ will be negative reciprocal of $-\frac{2}{3}$.

$\text{negative reciprocal of }-\frac{2}{3}=-(-\frac{3}{2})$

$\text{negative reciprocal of }-\frac{2}{3}=\frac{3}{2}$

Upon substituting $m=\frac{3}{2}$ and coordinates of point (8,1) in slope intercept form of equation we will get,

$1=\frac{3}{2}*8+b$

$1=3*4+b$

$1=12+b$

$1-12=12-12+b$

$-11=b$

Therefore, the equation $y=\frac{3}{2}x-11$ represents the equation of line perpendicular to our given line.

Answer 2

Answer:

The correct answer is: y=3/2x-11 :D