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Vilka [71]
2 years ago
15

Can someone help me please? It’s like my 3rd time trying to get some answers for this question. Thanks. :)

Mathematics
1 answer:
mote1985 [20]2 years ago
4 0

Answer:

both rates of change equal the slope of the line (3/4)

Step-by-step explanation:

Part a)

We calculate the rate of change using the formula:

\frac{y_2-y_1}{x_2-x_1}

for the first interval [0,6], we calculate the y-values at x=0 and x=6;

at x=0 : y=\frac{3}{2} (0)+2=2

at x=6 : y=\frac{3}{2} (6)+2=11

therefore, the rate of change in this interval is: \frac{y_2-y_1}{x_2-x_1}=\frac{11-2}{6-0}=\frac{9}{6} =\frac{3}{2}

For the second interval [-4,4], we calculate the y-values at x=-4 and x=4;

at x=-4 : y=\frac{3}{2} (-4)+2=-4

at x=4 : y=\frac{3}{2} (4)+2=8

therefore, the rate of change in this interval is: \frac{y_2-y_1}{x_2-x_1}=\frac{8-(-4)}{4-(-4)}=\frac{12}{8} =\frac{3}{2}

Part b):

Notice that both rates of change equal the value of the slope of the linear function (3/2)

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