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.