Question

Identify an equation in point slope form for the perpindicular to y=-3x+5 that passes through (4,-1)

Answer 1

Answer:

$\boxed {y = \dfrac{1}{3}x - \dfrac{7}{3}}$

Step-by-step explanation:

If we have a line y = mx + b where m is the slope and be is the y-intercept then a line perpendicular to this line will have slope -(1/m)

So the slope of the line perpendicular to y = -3x + 5 will be $-\dfrac{1}{3}$ = + 1/3 = 1/3

So the perpendicular line equation is

y = (1/3)x + b where b is the y intercept of this line

Since it passes through the point x = 4, y = -1 we plug in these values for x and y and solve for b

We get
$-1=\dfrac{1}{3}\cdot \:4+b$

Switch sides
$\dfrac{1}{3}\cdot \:4+b=-1$

$\dfrac{4}{3}+b=-1$

Subtract  $\dfrac{4}{3}$  from both sides

$b = -1 - \dfrac{4}{3} = -\dfrac{3}{3} -\dfrac{4}{3} = -\dfrac{7}{3}$

So the equation of the perpendicular line is
$\boxed {y = \dfrac{1}{3}x - \dfrac{7}{3}}$