Question

rate of change: -100
y = -100x + b
the initial value is the amount of air in
before it is deflated.
e is not given.
on the graph of the function?
(6,900)
(900,6)
(6,300)
(6, -300)
?
y = mx + b
rate of change
initial value
when the initial value is not given, you
can use the rate of change and a point
on the graph to find the value of b.

Explanation:

Step1: Recall the linear equation form

The equation is \( y = -100x + b \), and we need to check which point \((x,y)\) satisfies this equation. Let's test each point.

Step2: Test point \((6, 900)\)

Substitute \( x = 6 \) and \( y = 900 \) into \( y=-100x + b \):
\( 900=-100(6)+b \)
\( 900=-600 + b \)
\( b = 900 + 600=1500 \). Let's check if this makes sense, but let's test other points too.

Step3: Test point \((900, 6)\)

Substitute \( x = 900 \), \( y = 6 \):
\( 6=-100(900)+b \)
\( 6=-90000 + b \)
\( b = 90006 \). Unlikely for a deflation context (air amount), so discard.

Step4: Test point \((6, 300)\)

Substitute \( x = 6 \), \( y = 300 \):
\( 300=-100(6)+b \)
\( 300=-600 + b \)
\( b = 900 \). Not matching the first test's \( b \) if we assume a single \( b \), but wait, maybe the context is deflation (air decreasing over time, \( x \) as time, \( y \) as air). Let's re-examine. Wait, maybe the correct point is \((6, 900)\) or let's check the last point.

Step5: Test point \((6, -300)\)

Substitute \( x = 6 \), \( y = -300 \):
\( -300=-100(6)+b \)
\( -300=-600 + b \)
\( b = 300 \). Negative air doesn't make sense.

Wait, the initial value is air before deflation, so \( y \) should be positive. The point \((6, 900)\) gives \( b = 1500 \) (initial air), which is positive. But maybe I misread. Wait, the rate of change is -100 (air decreasing by 100 per unit time). If \( x = 6 \) (time 6), \( y = 900 \) (air left) makes sense: initial air \( b = 1500 \), after 6 units, \( 1500 - 600 = 900 \). So the point on the graph should satisfy \( y=-100x + b \), and \((6, 900)\) works.

Answer:

\((6, 900)\)