The graph of the linear function f(x) has a slope of -3/2 and a y-intercept of -1. write an equation for the function.

Cause it has a slope of -3/2, we could call its equation: y= -3/2x+b
and we have to find out b
In addition, it has a y-intercept of -1, that means this line goes through the point A(0;-1). So we could replace x=0 and y= -1:  -1 = -3/2x0+b and we have b= -1
We obtain the equation: y= -3/2x-1

Cross section is a rectangle.

Area of cross section = 16 sqrt(2) = 22.63 sq. units (to 2 decimals)

Step-by-step explanation:

Given a cube.

top face ABCD is parallel and congruent to bottom face EFGH  (1)

justified by the properties of cubes

Sides AE and CH are perpendicular to faces ABCD and EFGH (2)

justified by the properties of cubes

Diagonals AC and EH are congruent (3)

justified by (1), congruent top and bottom faces  

Consider cross-section ACHE

AC is congruent and parallel to  EH   (1) & (3)

EA & HC are perpendicular to AC      (2)

Therefore the quadrilateral ACHE is a rectangle.

Length of diagonal AC = sqrt(4^2+4^2) = 4 sqrt(2)  pythagoras theorem

AE = CH = DG = 4      properties of cube, all sides equal

Area of ACHE = 4* 4sqrt(2) = 16 sqrt(2) = 22.63 sq. units