Question

Start by finding the change in vertical distance from (45, 350) to (95, 75). That’s the same as the change in y-values of these points.

x
y
(95,
75
​
)
(45,
350
​
)
0
10
20
30
40
50
60
70
80
90
100
0
50
100
150
200
250
300
350
Time (min)
Temperature (°F)
Slope
=
vertical distance
horizontal distance
=
change in y-values
change in x-values

Answer 1

To find the change in vertical distance (change in y-values) from the point (45, 350) to the point (95, 75), we first note the y-values of these two points:

1. At \(x = 45\), \(y = 350\).
2. At \(x = 95\), \(y = 75\).

The change in y-values can be calculated as follows:

\[
\text{Change in y} = y_2 - y_1 = 75 - 350 = -275
\]

Next, we calculate the change in the x-values:

1. At \(x = 45\), we have \(x_1 = 45\).
2. At \(x = 95\), we have \(x_2 = 95\).

The change in x-values is:

\[
\text{Change in x} = x_2 - x_1 = 95 - 45 = 50
\]

Now we can find the slope, which is calculated using the formula for slope:

\[
\text{Slope} = \frac{\text{Change in y}}{\text{Change in x}} = \frac{-275}{50}
\]

Calculating this gives:

\[
\text{Slope} = -5.5
\]

Thus, the slope of the line connecting the two points is \(-5.5\).