Graph the line that represents a proportional relationship between y and x where the unit rate of change of y with respect to x is 4/5. In other words, a change of 1 unit in x corresponds to change of 4/5 units in y. Graph the line and write the equation of the line.

The required line is will be:

The graph of the line y = 4/5x is attached below.

Step-by-step explanation:

We know that when y varies directly with x, we get the equation

y ∝ x

y = kx

k = y/x

where k is called the 'constant of variation'.

It is also clear that 'constant of variation' basically represents the slope m or rate of change, with the lines passing through the origin, so

given

k = 4/5

substitute k = 4/5 in the equation y = kx

y = kx

y = 4/5x

Therefore, the required line is will be:

The graph of the line y = 4/5x is attached below.

- 2 + 10x³ - 21x² + 19x - 4

step-by-step explanation:

each term in the second factor is multiplied by each term in the first factor

x²(- 2x² + 4x - 1) - 3x(- 2x² + 4x - 1) + 4(- 2x² + 4x - 1) ← distribute

= - 2 + 4x³ - x² + 6x³ - 12x² + 3x -8x² + 16x - 4

collect like terms

= - 2 + 10x³ - 21x² + 19x - 4 ← in standard form