Write the slope intercept form of the equation of the line that passes through the points...

slope intercept form --> y = mx + b where m is the slope of the line and b is the y intercept.
the y intercept is where the line crosses the y (vertical) axis.
I can find the slope and the y intercept with this equation form

to do this problem you first have you use a different form of equation. it is called point slope form.
It uses a point on the line, and the slope
point slope form --> (y - y1) = m(x - x1) where m is the slope and (x1, y1) is a point on the line

(y - 4) = (-1)(x - (-5)) --> i just inserted (- 5, 4) for x1 and y1, and m = -1 into the equation.

there are a lot of negatives on the x side, so lets take it one step at a time

y - 4 = (-1) ( x + 5) --> now distribute the (-1) slope

y - 4 = - x - 5 --> add 4 to both sides

y = - x - 1 --> this is slope intercept form. the coefficient of x is the slope and m = -1
the y intercept is the number added or subtracted from x, b = -1

Write the slope intercept form of the equation of the line that passes through the point (-5, 4) and has a slope of -1.

Please explain. I have had the hardent time trying to understand how to do this.
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y = mx + B, where B is the y-intercept.

if slope = -1, then partial eq. is y = -x + B.

plug in your x and y for the one point to get B.

4 = -(-5) + B; 4 = 5 + B; B = -1.

final equation: y = -1x -1.

Ok, slope-intercept form is y=mx + b, with m equaling the slope and b equaling the y-intercept
m=-1; that's given to us
Plug in the coordinate (-5,4) with -5=x and 4=y
4=-1(-5) + b
4=5 + b
b= -1
Now, the whole equation is y= -x - 1

y = mx + b
m=slope
b= y intercept

(-5,4) plug these in

4 = (-1)*(-5) + b [-1 was slope given in your question]
4=5+b
4-5=5-5 +b [-5 both sides]
-1 = b [now right your equations but leave y as y and x as x]

y = -x - 1