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