write an equation in slope intercept form for the line that passes through the points (3,2) and(-9,6)

Mathematics

1 answer:

netineya [11]2 years ago

4 0

Answer:

y = - $\frac{1}{3}$ x + 3

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

Calculate m using the slope formula

m = (y₂ - y₁ ) / (x₂ - x₁ )

with (x₁, y₁ ) = (3, 2) and (x₂, y₂ ) = (- 9, 6)

m = $\frac{6-2}{-9-3}$ = $\frac{4}{-12}$ = - $\frac{1}{3}$ , hence

y = - $\frac{1}{3}$ x + c ← is the partial equation

To find c substitute either of the 2 points into the partial equation

Using (- 9, 6), then

6 = 3 + c ⇒ c = 6 - 3 = 3

y = - $\frac{1}{3}$ x + 3 ← in slope- intercept form

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3 years ago

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Write the vector u as a sum of two orthogonal vectors, one of which is the vector projection of u onto v, projvu u=(-8,8) , v= (

Jobisdone [24]

Answer:

none of the given options is true

Step-by-step explanation:

Given: u=(-8,8) , v= (-1,2)

To find: vectors $w_1,w_2$ such that $u=w_1+w_2$

Solution:

A vector is a quantity that has both magnitude and direction.

$proj_vu=\frac{u\cdot v}{\left | v \right |^2}(v)\\=\frac{(-8,8)\cdot (-1,2)}{(\sqrt{ (-1)^2+2^2})^2}(-1,2)\\=\frac{8+16}{5}(-1,2)\\=\frac{1}{5}(-24,48)\\=(-4.8,9.6)$