Light truck is a vehicle classification for trucks weighing up to
8500 pounds. In 2011, 5.919 million light trucks were sold in the U.S. In 2017, 11.055 million light trucks were sold. Write an equation in point-slope form that
represents the number of light trucks y sold y vears after 2010
To write an equation in point-slope form that represents the number of light trucks sold (y) years after 2010, we can use the given data points (2011, 5.919 million) and (2017, 11.055 million).
First, let's calculate the change in the number of light trucks sold over the 6-year period:
Change in y: 11.055 million - 5.919 million = 5.136 million
Change in x (years): 2017 - 2011 = 6
Next, let's calculate the slope (m) using the formula:
m = (change in y) / (change in x)
m = 5.136 million / 6
Now, we can substitute the values into the point-slope form equation:
y - y1 = m(x - x1)
Using the point (2011, 5.919 million):
y - 5.919 = (5.136 million / 6)(x - 2011)
Simplifying the equation gives us the final answer:
y - 5.919 = (0.856 million)(x - 2011)
So, the equation in point-slope form that represents the number of light trucks sold y years after 2010 is:
y - 5.919 = 0.856 million(x - 2011)
To write an equation in point-slope form, we need to know the slope and a point on the line. Let's begin by determining the slope.
The slope can be found by calculating the change in y (number of light trucks) divided by the change in x (years).
change in y = 11.055 million - 5.919 million = 5.136 million
change in x = 2017 - 2011 = 6
slope = change in y / change in x = 5.136 million / 6 = 0.856 million
Now that we have the slope, we can choose a point on the line. Let's use the point (2011, 5.919 million).
Using the point-slope formula:
y - y₁ = m(x - x₁)
where:
y₁ = 5.919 million
x₁ = 2011
m = 0.856 million
Plugging in the values:
y - 5.919 = 0.856(x - 2011)
This is the equation in point-slope form representing the number of light trucks sold y years after 2010.