Create an equation in slope-intercept form for the line that passes through (3, 6) and (6, 10).

y = 4/3x + 2

Step-by-step explanation:

Use the slope form of y2 - y1/ x2 - x1 and substitute in the values from the coordinates. In this case, it would be 10-6/6-3, which gives you 4/3. Thus, that would be the slope(m). Then take a pair of coordinates (x,y) and substitute in the equation y = mx + b.

If you take the first coordinate (3,6): 6 = 3(4/3) + b

                                                                6 = 4 + b

                                                                    b = 2

If you take the second coordinate (6, 10) : 10 = 6(4/3) + b

                                                                         10 = 8 + b

                                                                              b = 2

Then, substitute m and b into the equation (y = mx + b) to get your answer.

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.

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