Question

a rectangular box measures 6ft by 8ft by 2ft. Explain whether doubling a side from 6ft to 12ft would double the volume of the box.

Answer 1

V1 = 6*8*2 = 96
V2 = 12*8*2 = 192 = 2(96)

Answer 2

in general
V= s1*s2*s3 so if s1 is doubled ----> 2s1
the volume would become
V= (2s1)*s2*23
= 2*(s1*s2*s3)

Answer 3

Equation 4x+62y=8 describes a sloping line. For any
equation ax+by+c = 0, slope is - a/b = - 4/62 .
X intercept is found by setting y to 0: ax+by=c becomes ax=c. that means that x = c/a. 8/4 = 2.
Y intercept is found by setting x to 0: the equation becomes by=c, and therefore y = c/b. Y intercept is 8/62 = 0.129032258064516.
Slope is -4/62 = -0.0645161290322581.
Equation in slope-intercept form: y=-0.0645161290322581*x+0.129032258064516.

Answer 4

the volume of the box (not rectangle) is doubled. For any sides a,b,c, if the volume is abc and we replace a with 2a, the volume is (2a)bc = 2(abc).