Given two points (x₁,y₁) and (x₂,y₂); the slope of the line passes through these points is:
m=(y₂-y₁)/(x₂-x₁)
Point-slope form of a line: We need a point (x₀,y₀) and the slope "m".
y-y₀=m(x-x₀)
1) We calculate the slope:
(0,2)
(20,7)
m=(7-2)/(20-0)=5/20=1/4
2) We find out the equation of the line:
We can choose either two points : (0,2) or (20,7)
(0,2)
m=1/4
y-y₀=m(x-x₀)
y-2=1/4(x-0)
y-2=1/4 x
y=1/4 x+2 (slope-intercept form (y=mx+b))
Answer: The equation of the line is y=1/4 x+2
Now, we compute the cost of producing 50 engines:
if =x=50 ⇒ y=50/4+2=14.5
answer: The total cost of producing 50 engines is $14,500