Answer:
The y-intercept represents a temperature of 30°F when there are 0 cricket chirps.
The slope represents an additional 1 chirp for each addition 1.2°F increase in temperature.
If the number of chirps increases from 10 to 30, the temperature has increased by 24°F.
If the temperature increases from 30°F to 60°F, the number of chirps has increased by 25 chirps.
Explanation:
The given equation of the line of best fit is y = 1.2x + 30.
This is in slope-intercept form y = mx + b, where m is the slope and b is the y-intercept.
Therefore, for the given equation:
- slope = 1.2
- y-intercept = 30
Part (a)
The y-intercept is the point at which the graph intersects the y-axis, so the y-value when x = 0. Therefore:
- The y-intercept represents a temperature of 30°F when there are 0 cricket chirps.
Part (b)
The x-values represents the number of cricket chirps and the y-values represent the temperature in °F.
The slope tells us the rate of change of y relative to x, so the rate of change of the temperature to the number of cricket chirps.
1.2x means that for each increase of one x-value, the y-value increases by 1.2. Therefore:
- The slope represents an additional 1 chirp for each addition 1.2°F increase in temperature.
Part (c)
To find the temperature when the number of chirps is 10, substitute x = 10 into the equation of the line and solve for y:
⇒ y = 1.2(10) + 30 = 42°F
To find the temperature when the number of chirps is 30, substitute x = 30 into the equation of the line and solve for y:
⇒ y = 1.2(30) + 30 = 66°F
Therefore, the difference in temperature is:
⇒ 66°F - 42°F = 24°F
Therefore,
- If the number of chirps increases from 10 to 30, the temperature has increased by 24°F.
Part (d)
To find the number of chirps when the temperature is 30°F, substitute y = 30 into the equation of the line and solve for x:
⇒ 1.2x + 30 = 30
⇒ 1.2x = 0
⇒ x = 0
To find the number of chirps when the temperature is 60°F, substitute y = 60 into the equation of the line and solve for x:
⇒ 1.2x + 30 = 60
⇒ 1.2x = 30
⇒ x = 25
The difference in the number of chirps is:
⇒ 25 - 0 = 25
Therefore,
- If the temperature increases from 30°F to 60°F, the number of chirps has increased by 25 chirps.