Interpreting Algebraic Models Question 10

The phase diagram above shows the conditions that are needed to form different aluminosilicate minerals. The temperature $T$ , in degrees Celcius (°C) is shown on the horizontal axis, and the pressure $P$ , in gigapascals (GPA), is shown on the vertical axis. An equation of the boundary line between the andalusite and sillimanite regions is approximated by the equation below. What is the meaning of the $T$ -intercept of this line?

P=-0.00146T+1.11

The maximum pressure at which both andalusite and sillimanite can form.

The temperature at which both andalusite and sillimanite can form when there is no pressure applied.

The number of degrees Celsius needed to remain on the boundary between andalusite and kyanite if the pressure is reduced by 1 GPa.

The decrease in the number of gigapascals of pressure needed to remain on the boundary between andalusite and sillimanite if the temperature is increased by 1 °C.

Approach 1

We can interpret the meaning of the $T$ -intercept by comparing it to a more familiar scenario.

Pressure vs. Temperature

\bold{P}=m\bold{T}+b

The

T

-intercept would be the point where the

P

value is equal to zero.

y

vs.

x

\bold{y}=m\bold{x}+b

The

x

-intercept would be the point where the

y

value is equal to zero.

We can calculate this algebraically, but instead we can utilize the graph. There is only one point where the Pressure $P$ is 0.

This point seems to correspond to a point on the line where both sillimanite and andalusite can form (boundary line). The answer choice also emphasizes that it is when the pressure is zero:

○ The temperature at which both andalusite and sillimanite can form when there is no pressure applied.

Approach 2

The first choice refers to pressure, so it cannot be associated with the $T$ -intercept, which would give a value related to temperature. The last two answer choices are described as rates rather than a constant. They may be suitable answer choices if the question were asking for the meaning of something related to slope. The correct answer choice refers to temperature, which is correctly associated with the $T$ -intercept.