Find the eqation of the line perpendicular to y=3x-6 that runs through the point (2, 3)

y = -1/3x + 3.7

Step-by-step explanation:

To find the equation of the line perpendicular to y = 3x - 6, you first need to find the slope. The slope of a line perpendicular to another will always be the opposite value and reciprocal of the other line.

In this case, the slope 3, or 3/1 has a perpendicular slope of -1/3

Now, we need to find the y-intercept. To do that, we will use the equation y = mx + b, the slope -1/3, and our given point (2,3). Y is our y-coordinate, m is the slope, x is our x-coordinate, and b is the y-intercept.

First, we plug in the values:

3 = -1/3(2) + b

Simplfy.

3 = -2/3 + b

Add 2/3 to both sides.

3 + 2/3 = -2/3 + 2/3 + b

Combine like terms.

3 2/3 = b

Simplify.

3 2/3 = 11/3 = 3.7 (3.66666666... rounded to the nearest tenth)

b = 3.7

Now, we put everything together!

The equation to the line perpendicular to y = 3x - 6 that runs through the point (2,3) is y = -1/3x + 3.7

step-by-step explanation:

option a, c,d are correct.

step-by-step explanation:

from the given figure, it is given that z is equidistant from the sides of the triangle rst, then from triangle tzb and triangle szb, we have

tz=sz(given)

bz=zb(common)

therefore, by rhs rule,δtzb ≅δszb

by cpctc, sz≅tz

also, from δctz and δasz,

tz=sz(given)

∠tcz=∠saz(90°)

by rhs rule, δctz ≅ δasz, therefore by cpctc, ∠ctz≅∠asz

also,from δasz and δzsb,

zs=sz(common)

∠zbs=∠saz=90°

by rhs rule, δasz ≅δzsb, therefore, by cpctc, ∠asz≅∠zsb

hence, option a, c,d are correct.