Recent studies indicate that the average surface temperature...

Recent studies indicate that the average surface temperature of the earth has been rising steadily. Some scientists have modeled the temperature by the linear function $T=0.02 t+8.50 .$ where $T$ is temperature in $^{-} \mathrm{C}$ and $t$ represents years since $1900 .$ (a) What do the slope and $T$ -intercept represent? (b) Use the equation to predict the average global surface temperature in 2100.

Recent studies indicate that the average surface temperature of the earth has been rising steadily. Some scientists have modeled the temperature by the linear function $T=0.02 t+8.50 .$ where $T$ is temperature in $^{-} \mathrm{C}$ and $t$ represents years since $1900 .$
(a) What do the slope and $T$ -intercept represent?
(b) Use the equation to predict the average global surface temperature in 2100.

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Key Concepts

Prediction Using Linear Models

Linear models are used to predict future values by substituting the desired input value into the equation. This allows for estimation of outcomes based on the established linear trend, making them useful for forecasting in various scenarios where past trends are expected to continue.

Slope in Linear Models

The slope in a linear equation represents the rate at which the dependent variable changes with respect to the independent variable. In modeling scenarios, it quantifies how much the output (such as temperature) increases or decreases for each unit increase in the input (such as time), providing a measure of the trend or change rate in the data over time.

Y-Intercept in Linear Models

The y-intercept is the value of the dependent variable when the independent variable is zero. It indicates the starting point of the modeled relationship, showing the initial or baseline value of the quantity being measured before any changes are applied due to the independent variable.

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