What's the equation of a line that passes through points (–1, –5) and (1, 3)?
2 answers:
Answer:
y = 4x - 1
Step-by-step explanation:
The equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
Calculate m using the slope formula
m =
with (x₁, y₁ ) = (- 1, - 5) and (x₂, y₂ ) = (1, 3)
m = =
= 4 , then
y = 4x + c ← is the partial equation
To find c substitute either of the 2 points into the partial equation
Using (1, 3 ) , then
3 = 4 + c ⇒ c = 3 - 4 = - 1
y = 4x - 1 ← equation of line
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Answer:
Step-by-step explanation:
Volume =
find partial derivatives using product rule
i.e.
Using maximum for partial derivatives, we equate first partial derivative to 0.
y=0 or x+y =6
x=0 or x+4y =12
Simplify to get y =2, x = 4
thus critical points are (4,2) (6,0) (0,3)
Of these D the II derivative test gives
D<0 only for (4,2)
Hence maximum volume is when x=4, y=2, z= 4/3
Max volume is = 4(2)(4/3) = 32/3