To find the slope \( m \) of the line that passes through the two points (6, 150) and (11, 250), we can use the slope formula:
\[ m = \frac{y_2 - y_1}{x_2 - x_1} \]
Using the given points:
- \( (x_1, y_1) = (6, 150) \)
- \( (x_2, y_2) = (11, 250) \)
Substituting the values into the slope formula:
\[ m = \frac{250 - 150}{11 - 6} = \frac{100}{5} = 20 \]
Thus, the slope \( m \) is 20. This means the temperature increases by 20 degrees Fahrenheit for each minute.
Now that we have the slope, we can use point-slope form to find the equation of the line in the form \( y = mx + b \). We can use one of the points (let's use (6, 150)) to find \( b \).
Starting with the slope-intercept form:
\[ y = mx + b \]
Substituting \( m \) and one of the points:
\[ 150 = 20(6) + b \]
Calculating the right side:
\[ 150 = 120 + b \]
Solving for \( b \):
\[ b = 150 - 120 = 30 \]
Now we can write the equation of the line:
\[ y = 20x + 30 \]
Final answer:
- Slope \( m = 20 \)
- Equation: \( y = 20x + 30 \)