Write down the gradient of the straight line represented by the equation w = 0.54t − 0.4. What does this measure in the practical situation being modelled?

Sure, let's break it down step by step.

1. Identify the equation of the straight line: $w = 0.54t - 0.4$

2. Recognize the standard form of a linear equation: $y = mx + c$ where $m$ is the gradient (slope) and $c$ is the y-intercept.

3. Compare the given equation with the standard form: Here, $w$ corresponds to $y$ and $t$ corresponds to $x$. Therefore, the gradient $m$ is 0.54.

4. Write down the gradient: The gradient of the straight line is 0.54.

5. Interpret the gradient in the practical situation: The gradient measures the rate of change of $w$ with respect to $t$. In other words, for every unit increase in $t$, $w$ increases by 0.54 units. This indicates how quickly $w$ changes as $t$ changes in the context of the model.