Question

The table represents a linear function. The rate of change between the points (–5, 10) and (–4, 5) is –5. What is the rate of change between the points (–3, 0) and (–2, –5)? x y –5 10 –4 5 –3 0 –2 –5 –5

Answer 1

The rate of change between the points (-3,0) and (-2,-5) is -5, equal to the rate of change between the points (-5,10) and (-4,5), because it is a linear function.

Explanation:

The rate of change between the points (-3,0) and (-2,-5) is -5, equal to the rate of change between the points (-5,10) and (-4,5), because it is a linear function. Let's check:

Rate of change "r" between the points (xa,ya) and (xb,yb) is:

r = (yb-ya) / (xb,xa)

In this case the points are:

(-3,0)=(xa,ya)→xa=-3, ya=0

(-2,-5)=(xb,yb)→xb=-2, yb=-5

then, replacing the values in the formula:

r = (-5-0) / (-2-(-3))

r = (-5) / (-2+3)

r = (-5) / (1)

r = -5