What is the equation of the line that passes through the point ( -4, 2) and has a slope of
-2?

The equation is: y = -2x -6

Step-by-step explanation:

We have the slope which is - 2. This the main form of a straight line equation is: y = mx + c

y = y point (2)

m = slope (-2)

x = x point (-4)

c = constant - this you need to work out!

Firstly we arrange the equation: y = mx + c

We substitute or replace what we already know into this equation. It is like building a puzzle and only the last piece is unknown and we are trying to make this last piece fit into this puzzle.

The only thing we don't know is what c equals to. After substituting, we get

y = -2x + c.

We can further substitute x and y which is the point (-4;2), we then get:

2 = - 2(- 4) + C

and by using simple math by taking the

- 2(- 4) (which equals to +8, since multiplying 2 negative numbers give you a positive number) to the other side which becomes negative, will give you c = - 6.

Then sub C into the equation.

Hope this helps. :)

8

step-by-step explanation:

let f (x ) is a function and c be a positive real number,   the graph of the function g (x ) = f (cx ) is represented as follows.

when, c > 1,   the function compresses it in the x - direction.

when, 0 < c < 1, the function stretches it.

the function is g ( x ) = (9x )2.

the heighest power of x in g ( x ) = (9x )2 is 2, so the parent function is square function.

the equation of parent function is f ( x ) = x 2 .

the function is g ( x ) = (9x )2 and the parent function is f ( x ) = x 2 .

so, the functions f and g have the following relationship.

g ( x ) = f ( 9x ).

compare the function g ( x ) = f ( 9x ) with g (x ) = f (cx ).

c = 9 ( > 1 ).

so, the function g (x ) = (9x )2 compresses it in the x - direction.

step-by-step explanation: