The problem states that the temperature at sunrise is 40°F and that it rises by 4°F each hour. You are asked to model this situation with an equation that expresses the temperature, $y$, after $x$ hours.

This is a linear equation because the temperature increases at a constant rate. The general form of a linear equation is:

$y = mx + b$

Where:

• $y$ is the temperature after $x$ hours,
• $m$ is the rate of change (the temperature rise per hour),
• $b$ is the initial temperature at sunrise.

Given:

• The temperature increases by 4°F per hour, so $m = 4$,
• The initial temperature is 40°F at sunrise, so $b = 40$.

Thus, the equation becomes:

$y = 4x + 40$

This equation models the temperature $y$ (in °F) after $x$ hours.

Graph:

The graph of this equation will be a straight line with a slope of 4 and a y-intercept at 40. It starts at the point (0, 40) on the y-axis and rises by 4 units for every 1 unit increase in $x$, representing the increase in temperature over time.

Do you want further details or clarification?

Related Questions:

1. How would the equation change if the temperature rose by 6°F each hour instead of 4°F?
2. What is the temperature after 5 hours?
3. After how many hours will the temperature reach 60°F?
4. How does the slope of the line relate to the rate of temperature increase?
5. How can we modify this model if the temperature rise is not constant?

Tip:

In linear equations, the slope represents the rate of change, and the y-intercept represents the starting value of the dependent variable.