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Derive and Interpret y = mx + b
A function can be used to measure the time it takes to preheat an oven.
1. Francisco checks the temperature of the oven two times. The first time he
checks the temperature is 4 minutes after he starts preheating the oven.
The temperature is 158 °F. The second time is 7 minutes after he starts
preheating the oven. The temperature is 224 °E.-
A. How many degrees does the temperature of the oven increase by in
one minute?

User Shameen
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1 Answer

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Answer:

To find the number of degrees the temperature of the oven increases by in one minute, we can use the slope-intercept form of a linear equation, which is written as y = mx + b. In this equation, y represents the dependent variable (in this case, the temperature of the oven), x represents the independent variable (in this case, the time in minutes), m is the slope (which represents the rate of change of y with respect to x), and b is the y-intercept (which represents the starting value of y when x is zero).

To find the slope of the line that represents the temperature of the oven over time, we can use the two points provided in the problem: (4, 158) and (7, 224). The slope is calculated using the following formula:

m = (y2 - y1) / (x2 - x1)

Plugging in the values from the two points, we get:

m = (224 - 158) / (7 - 4) = 66 / 3 = 22

This means that the temperature of the oven increases by 22 degrees for every one minute increase in time.

The y-intercept of the line (the value of y when x is zero) represents the starting temperature of the oven. In this case, the starting temperature is not provided, so we cannot determine the y-intercept. However, we can use the slope and one of the points to find the equation of the line in the form y = mx + b:

y = 22x + b

Substituting one of the points into the equation, we get:

158 = 22 * 4 + b

Solving for b, we get:

b = 158 - 88 = 70

So the equation of the line representing the temperature of the oven over time is:

y = 22x + 70

This equation tells us that for every one minute increase in time, the temperature of the oven increases by 22 degrees, starting from a temperature of 70 degrees.

User Adam Szabo
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