1) we find the slope of this line:
Given two points, (x₁,y₁) and (x₂,y₂) the slope of the line passes through these points will be:
m=(y₂-y₁)/(x₂-x₁)
In this case, we have the points (1,4) and (5,8) and the slope will be:
m=(8-4)/(5-1)=4/4=1
2)Point-slope form of a line:
We need a point (x₀,y₀) and the slope (m);
y-y₀=m(x-x₀)
we can chooso either point of this line (1,4) or (5,8) the end result will be the same.
For example, we choose the point (1,4);
y-y₀=m(x-x₀)
y-4=1(x-1) (point-slope form y-y₀=m(x-x₀))
y=x-1+4
y=x+3 (slope-intercept form y=mx+b)
-x+y=3 (standard form Ax+By=C)
if we choose the point (5,8)
y-8=1(x-5) (point-slope form)
y=x-5+8
y=x+3
-x+y=3
Therefore:
Answer: D. -x+y=3
