The slope of a line is defined as the change in y divided by the change in x:

Slope=`(Deltay)/(Deltax)`

Given a point `(x_1,y_1)`, the change in y can be written as

`Deltay=y-y_1`

And the change in x can be written as:

`Deltax=x-x_1`

The equation of the line can then be written:

`y-y_1=(Slope)(x-x_1)`

In `y-(-4)=-4(x-2)` the point `(x_1,y_1)` is equal to (2,-4) and the slope is equal to -4.

Therefore the line passes through the point (2,-4) and this point is the basis of this equation.

The slope intercept form is y=mx+b, where m is the slope and b is the y intercept. To write the slope intercept method, solve for y.

`y+4=-4(x-2)`

`y=-4x+8-4`

`y=-4x+4`             (1)

Thus the slope is -4 and the y intercept is 4.

The standard form of a line is: ax+by=c. Add 4x to both sides of (1).

`4x+y=4`

To determine the x intercept, substitute 0 for y.

`4x=4`

`x=1`

Thus the x intercept is 1.

Graph:

The equation of the line y + 4 = -4*(x - 2) is in the point slope form. Rewriting the equation `(y+4)/(x - 2) = -4` . The slope of this line is -4 and it passes through the point (2, -4).

y + 4 = -4*(x - 2)

=> y + 4 = -4x + 8

=> y = -4x + 4

This is the equation in the slope-intercept form.

At the x-intercept the y-coordinate is 0.

0 = -4x + 4

=> x = 1

The x-intercept of the line is 1.