Agroup of workers is harvesting berries at a constant rate. an equation that represents the number of baskets of berries the workers picked over a period of time, in hours, is y = 6x + 8. (a) what are the slope and the y-intercept for the equation that represents the number of baskets of berries the workers picked over a period of time? (b) what are the rate of change and the initial amount? explain the meaning of the rate of change and the initial amount for the situation. (c) use graph paper to draw a graph representing the situation. label the axes appropriately.

Question: (a) What are the slope and the y-intercept for the equation that represents the number of baskets of berries the workers picked over a period of time?

Given equation is y = 6x + 8.

Where y represents the number of baskets of berries the workers picked over a period of time x in hours.

Compare with slope intercept form y=mx+b, we get m=6 and b=8

Hence slope is 6 and y-intercept is 8.

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Question: (b) What are the rate of change and the initial amount? Explain the meaning of the rate of change and the initial amount for the situation.

Rate of change means slope so answer is 6.

Initial amount means y-intercept so that is 8.

rate of change of 6 means six baskets of berries are picked by workers in 1 hour.

Initial amount of 8 means there was 8 baskets of berries already filled in the beginning.

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Question: (c) Use graph paper to draw a graph representing the situation. Label the axes appropriately.

first we graph y-intercept that is at point (0,8)

slope = 6 means make another point which is 6 unit up then 1 unit right from (0,8) so the new point is at (1,14)

Hence final graph is the line joining both points.

b

step-by-step explanation:

x= -3 and

step-by-step explanation:

to find the roots of a cubic, use division or factoring to find the factors then set equal to 0. as this is a difference of cubes, it factors into

where a is the cube root of .

here   this is 27 and the cube root of 27 is 3. so we write using the form:

.

set each factor to 0 and solve for x.

x-3=0

x=3

the quadratic expression does not factor and must be solved using the quadratic formula.

where a = 1, b=3, and c=9

this cubic has two complex roots.