The parent function, f(x) = 5x, has been vertically compressed by a factor of one-half, shifted to the right three units and up two units.

I'm guessing you want to know what the new function looks like.

Compression takes place when you have a function that constant is between 0 and 1

so f(x) = 1/2 5x We'd best not do any more to it for now because it will be altered by the next two transformations.

You want to shift this to the right two units.

That means f(x-2) will bu put into x on the right. You will get

f(x - 2) = 1/2*5(x - 2)

Finally, we want to go up 2 units.  That's done by adding another term on what we have already.

f(x -2)  = 1/2 * 5(x - 2) + 2

A line is not a very good example to be showing these transformations. I'll include a graph.

The red line is f(x) = 5x

The blue line is f(x - 2) = 1/2 * 5(x -2) + 2

step-by-step explanation:

the shape,the size and the distance

5x + 3y = - 4

step-by-step explanation:

the equation of a line in standard form is

ax + by = c ( a is a positive integer and b, c are integers )

express the line first of all in slope- intercept form

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

to calculate m use the gradient formula

m = ( y₂ - y₁ ) / ( x₂ - x₁ )

with (x₁, y₁ ) = (7, - 3) and (x₂, y₂ ) = (4, - 8)

m = = -

y = - x + c ← is the partial equation

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

using (4, - 8 ), then

- 8 = - + c ⇒ c = -

y = - x - ← in slope-intercept form

multiply all terms by 3 to eliminate the fractions

3y = - 5x - 4 ( add 5x to both sides )

5x + 3y = - 4 ← in standard form