Along the New York State Thruway there are distance markers...

Along the New York State Thruway there are distance markers that give the number of miles from the beginning of the thruway. Brianna enters the thruway at distance marker $150 .$ a. If $\mathrm{m}(x)=$ the number of miles that Brianna has traveled on the thruway, write an equation for $\mathrm{m}(x)$ when she is at distance marker $x$ . b. Write an equation for $\mathrm{h}(x),$ the number of hours Brianna required to travel to distance marker $x$ at 65 miles per hour

Along the New York State Thruway there are distance markers that give the number of miles from the beginning of the thruway. Brianna enters the thruway at distance marker $150 .$
a. If $\mathrm{m}(x)=$ the number of miles that Brianna has traveled on the thruway, write an equation for $\mathrm{m}(x)$ when she is at distance marker $x$ .
b. Write an equation for $\mathrm{h}(x),$ the number of hours Brianna required to travel to distance marker $x$ at 65 miles per hour

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Key Concepts

Linear Functions

A linear function models a relationship where one quantity changes at a constant rate with respect to another. In many real-world contexts, such as measuring distance traveled or time elapsed, linear functions simplify the relationship into an equation of the form f(x) = mx + b.

Initial Value (Intercept)

In a linear function, the initial value or y-intercept represents the starting point of the measurement before any changes occur. This concept is key when a journey or process does not start at zero and you must account for that initial offset in the equation.

Rate of Change (Slope)

The rate of change, or slope, in a linear function indicates how fast one variable increases or decreases relative to another. It is crucial in scenarios like travel where the slope represents constant speeds and determines how the distance changes over time.

Distance-Time Relationship

The distance-time relationship applies the principle that distance equals speed multiplied by time. This relationship is fundamental in problems involving uniform motion, connecting rates (such as miles per hour) to distances traveled over time.

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