Given two points (x₁,y₁) and (x₂,y₂), the slope of the line passes throught of these points will be:
m=(y₂-y₁)/(x₂-x₁)
If we want to find the equation of a line, we only need a point (x₀,y₀) and the slope:
Point-slope form: y-y₀=m(x-x₀)
a)
(6,1)
(5,4)
1)we find the slope of the line passes through these points.
m=(4-1)/5-6)=3/-1=-3
2)We find the equation of the line:
We can choose either points of two points
if we chose the point (5,4)
y-y₀=m(x-x₀)
y-4=-3(x-5) (point-slope form)
y-4=-3x+15
y=-3x+19 (slope intercept form)
Answer: the equation would be: y=-3x+19
b)
(8,1)
(7,9)
m=(9-1)/(7-8)=8/-1=-8
y-y₀=m(x-x₀)
y-1=-8(x-8)
y-1=-8x+64
y=-8x+64+1
y=-8x+65
Answer: y=-8x+65
