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?

Question

x
y
(2, 100)(6, 220)
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20
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60
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Time (minutes)
Temperature (°F)
y= mx + b

Slope =

Answer 1

To find the slope (m) of the line given the two points \((2, 100)\) and \((6, 220)\), we can use the formula for the slope between two points \((x_1, y_1)\) and \((x_2, y_2)\):

\[ m = \frac{y_2 - y_1}{x_2 - x_1} \]

Substituting the coordinates of the points into the formula, we get:

• Let \((x_1, y_1) = (2, 100)\) and \((x_2, y_2) = (6, 220)\).

\[ m = \frac{220 - 100}{6 - 2} \]

Calculating the values:

\[ m = \frac{120}{4} = 30 \]

So the slope \(m\) is 30. This means the temperature increases by 30 degrees Fahrenheit for every minute.

Next, we need to write the equation in the form \(y = mx + b\). We can use one of the points to find \(b\) (the y-intercept).

Using the point \((2, 100)\):

\[ 100 = 30(2) + b \]

Calculating:

\[ 100 = 60 + b \]

Now, solve for \(b\):

\[ b = 100 - 60 = 40 \]

Now that we have both \(m\) and \(b\), we can write the equation of the line:

\[ y = 30x + 40 \]

Summary:

• Slope (m) = 30
• Equation of the line: \(y = 30x + 40\)