(2,-3), slope = 4
What is the answer

We are given:

The line passes through (2,-3)

Slope of the line = 4

Finding the equation of the line:

We know that the general form of the slope-intercept form is:

y = mx + b         [where m is the slope and b is the y-intercept]

y = 4x + b          [since slope = 4]

Finding the y-intercept:

Now, we are given that the line passes through the points: (2,-3)

which can be written as: x = 2 and y = -3

Since the line passes through these points, these values must satisfy the equation

So,

y = 4x + b

-3 = 2(4) + b

-3 = 8 + b

b = -11                [subtracting 8 from both sides]

Hence, the y-intercept is -11

Equation of the line:

We wrote the equation of the line as:

y = 4x + b          (where b is the y-intercept)

now that we know the value of b,

y = 4x - 11

Therefore, the equation of the line is: y = 4x - 11

answer: ratio of volume of cone (with 3 times the height and equal diameter) to volume of cylinder is 2 to 1. the value of π is not used.

step-by-step explanation:

radius is diameter/2 = 4.

area of circle is π r^2.

volume of cylinder is height × area of base = hπr^2 = 3(4^2) π = 48π cubic inches.

not knowing the formula for volume of cone, i calculate it using calculus (which is for calculating things).

volume of cone is integral 0 to h area(y) dy. area(y) is π r(y)^2. r(y) runs r to zero as y runs zero to h, r(0) = r, r(h) = 0.

r(y) = r - r/h y

area(y) = π (r - r/h y)^2 = π (r^2 - 2r^2y/h + r^2y^2/h^2) = π r^2(1-2y/h+y^2/h^2)

antiderivative area(y) = π r^2 (y-y^2/h+y^3/(3h^2))

integral 0 to h = π r^2(h-h^2/h+h^3/(3h^2) - (0)) = π r^2(h - h + h/3) = π r^2(h/3) = π/3 r^2 h

volume of this cone is π/3(4^2)18 cubic inches.

= 6 16 π = 96π cubic inches.

cone has twice the volume, 96/48.

cone height is 6 times the cylinder.

ratio of volume formula: π r^2 cancels.

cone over cylinder ratio is 6h/3 to h, 2 to 1.