Substitute the slope, 10, for m in our equation.

Question

x
y
(4,60)
(2,40)
0
2
4
6
8
10
12
0
20
40
60
80
100
120
140
Number of minutes
Temperature (°C)
Slope 0 = 0 10
y 0 = 0 mx+b
y 0 = 0
x+b

Answer 1

To substitute the slope \( m = 10 \) into the linear equation \( y = mx + b \), you would modify the equation as follows:

\[ y = 10x + b \]

Now, to determine the value of \( b \) (the y-intercept), we can use one of the given points. Let's use the point \( (2, 40) \):

1. Substitute \( x = 2 \) and \( y = 40 \) into the equation:

   \[ 40 = 10(2) + b \] This simplifies to:

   \[ 40 = 20 + b \]

2. Now, solve for \( b \):

   \[ b = 40 - 20 = 20 \]

So, the equation of the line with the slope 10, using the point \( (2, 40) \), becomes:

\[ y = 10x + 20 \]

This is the linear equation that represents the relationship between the number of minutes (x) and temperature (°C) (y).

If you would like to check it with another point, you could verify that it holds true for \( (4, 60) \):

1. Substitute \( x = 4 \) into the equation:

   \[ y = 10(4) + 20 = 40 + 20 = 60 \]

This confirms that the equation \( y = 10x + 20 \) is consistent with both points \( (2, 40) \) and \( (4, 60) \).