Ella is preparing for a 20-mile endurance cycling competition. She practices by cycling at a constant speed of 12 miles per hour for the first 4 miles. She increases her speed by 1.5 miles per hour every mile until she reaches 12 miles. After crossing 12 miles, she reduces her speed by 3 miles per hour each mile, till she reaches a speed of 15 miles per hour and keeps it constant until the end of her ride.

From the graph shown below, find the interval where Ella's speed is increasing.

A.
Ella's speed is increasing between 12 and 15 miles.
B.
Ella's speed is increasing between 4 and 12 miles.
C.
Ella's speed is increasing between 16 and 18 miles.
D.
Ella's speed is increasing between 0 and 3 miles.

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