Question

Let’s write an equation to represent this line in the form y=mx+b. Start by finding m, or the slope. What is the slope of this line? In other words, what is the change in degrees for each minute?
x
y
(6, 150)(11, 250)
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Time (minutes)
Temperature (°F)
y= mx + b

Slope =

Answer 1

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: \( y = 20x + 30 \)