To create an equation that models the path of light from a car’s headlight, we can analyze the given vertical and horizontal distances. It looks like this path can be modeled by a linear equation.
We can start by examining the data points:
- (16, 1.3)
- (4.2, 0.1)
- (6, 0)
- (7.8, 0.1)
- (0, 1.3)
The vertical distance represents the height of the light above a base level (like ground), and the horizontal distance represents how far the light spreads horizontally.
To find the linear equation, we can use the two extreme points: (16, 1.3) and (0, 1.3) for consistent h values.
- Calculate the slope (m) using two points:
Let's take (16, 1.3) and (0, 1.3):
- The slope \( m \) = \( \frac{y_2 - y_1}{x_2 - x_1} \)
- Here, both y values are 1.3, so the slope comes out to be \( \frac{1.3 - 1.3}{16 - 0} = 0 \).
This gives us a horizontal line that indicates constant vertical distance.
Next, since the shape is consistent for a headlight, we find the maximum height (h) observed from the data points.
Looking through the table:
- The maximum height (vertical distance) is 1.3 feet.
Thus, the average heights used for modeling seem clustered at:
- h will be where it is the light's bright peak which mostly is 1.3 feet above.
So, rounding to the nearest hundredth: h = 1.30
In conclusion:
- In the equation that models this situation, h = 1.30.