Determine the slope and the y-intercept of the equation of the line passing through the points (-5, 3) and (1, -3). write the equation of the line in slope intercept form.

Given two points (x₁,y₁) and (x₂,y₂) the slope of the line passing through these points will be:

m=(y₂-y₁)/(x₂-x₁) 

Data:
(-5,3)
(1,-3)

m=(-3-3) / (1+5)=-6/6=-1

the slope would be m=-1.

Point slope form: we need only a point (x₀,y₀) and the slope "m",
y-y₀=m(x-x₀)

In this case:
The point can be (-5,3) or (1,-3), we can choose either of these points.
For example, if we choose the point (-5,3) the point-slope form will be:

y-y₀=m(x-x₀)
y-3=-1(x+5)
y-3=-x-5
y=-x-5+3
y=-x-2    (this is, slope-intercept form  : y=mx+b)

the equation of the line in slope intercept form is y=-x-2