The function in the table below shows the relationship between the total number of houses built in an area and the number of months that passed. the function in the table below shows the relationship between the total number of houses built in an area and the number of months that passed. which best describes the data set? it is nonlinear because the “total houses built” column does not increase at a constant additive rate. it is nonlinear because the “months passed” column does not increase at a constant additive rate. it is nonlinear because the increase in the “total houses built” compared to the increase in the “months passed” does not show a constant rate of change. it is linear because the increase in the “total houses built” compared to the increase in the “months passed” shows a constant rate of change.

A linear function will have the characteristic of constant changing rate for every unit

Between month 0 and month 3, the number of houses built is 33.
This means the changing rate is 33÷3 = 11 houses per month

Between month 3 and month 4, the number of houses built is 46
This means the changing rate is 46÷1 = 46 within the month

Between month 4 and month 8, the number of houses built is 108
This means the changing rate is 108÷4 = 27 houses per month

The changing rate does not show the same number of houses monthly, it means the function is not linear.

Correct C

and y≤ -x +4 .

step-by-step explanation:

we are given a graph for system of inequalities.

in order to write the system of inequalities for the given graph, we need to find the inequality for each of the line separately.

let us find the slope of dotted line first.

taking two coordinates on the graph.

let us say (0,0) and (3,1).

let us find the slope of the line now.

slope of the dotted line would be =.

y-intercept of dotted line is y=0 only.

plugging slope m= and b=0 in slope-intercept form y=mx+b, we get

.

the line is shaded up of that dotted line.

therefore, for shading up we would take greater than inequality symbol > .

and because it's a dotted line we would take only > symbol in place of = sign in above equation of line.

therefore, inequality for dotted line would be

.

let us take two points (3,1) and (0,4) on the solid line.

slope of the solid line would be =.

for the solid line we have y-intercept b= 4.

plugging slope m= -1 and b=4 in slope-intercept form y=mx+b, we get

y = -1x + 4.

the line is shaded down of that solid line.

therefore, for shading down we would take less than inequality symbol < .

and because it's a solid line we would take ≤ symbol in place of = sign in above equation of line.

therefore, inequality for solid line would be

y≤ -x +4 .

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