How to write the slope-intercept form of the equation of the line through the given points: (-1,-3) and (-4,5)

The slope-intercept form of a line is:

y=mx+b, where m=slope and b=y-intercept (value of y when x=0)

First you must find the slope, or m value.

m=(y2-y1)/(x2-x1), which is the change in y divided by the change in x.  In this case:

m=(5--3)/(-4--1)

m=(5+3)/(-4+1)

m=8/-3

m=-8/3

So far our line is:

y=-8x/3+b, we can now solve for the y-intercept, or b, using any point on the line, I'll use (-4,5):

5=-8(-4)/3+b

5=32/3+b

15/3=32/3+b

15/3-32/3=b

-17/3=b

So now we know the value for both terms in our line:

y=(-8x-17)/3