Question

Georgia filled her kitchen sink up with water so that she could do the dishes. When she was done with the dishes, she pulled out the drain stopper so the water could begin to drain out of the sink.

A linear model of this situation contains the values (2, 8.4) and (4, 7.8), where x represents the number of seconds, and y represents the water level in the sink, in inches.

What is the rate of change in this linear model?
A.
-0.3 of an inch per second
B.
0.3 of an inch per second
C.
-9 inches per second
D.
-0.6 of an inch per second

Answer 1

y = (-0.3 in/sec)x + 9.0 in

Explanation:

(2, 8.4) and (4, 7.8) are points on a linear graph.

As we go from (2, 8.4) to (4, 7.8), x increases by 2 and y decreases by 0.6.

Thus, the slope of the line is m = rise / run = -0.6 / 2, or m = -0.3 inches/sec

Let's use the slope-intercept form of the equation of a straight line, with m = -0.3 in/sec and one point being (2, 8.4).

Then y = mx + b becomes 8.4 = (-0.3 in/sec)(2) + b, or

8.4 = -0.6 + b. Thus, b = 9.0, and the desired equation is thus:

y = (-0.3 in/sec)x + 9.0 in

Answer 2

A) -0.3 of an inch per second

Explanation:

You'll have to put (2, 8.4) and (4, 7.8) into the slope formula.

It's represented as (∆y)/(∆x) = m

(y1 + y2)/(x1 + x2) = m

You subtract both y's in the numerator and subtract both x's in the denominator.

Like this:

(8.4-7.8)/(2-4) = m

(0.6)/(-2) = m

-0.3 = m