During a snowstorm, snow falls at a constant rate and is recorded by a meteorologist.  The data is plotted on the graph below.

The graph titled 'Snowstorm' with number of hours on horizontal x-axis from 0 to 5 in increments of 1 and inches of Snow on the ground on vertical y- axis from 0 to 30 in increments of 3. Points (0, 3), (5, 18) are connected through a line.

Which equation models the relationship between the number of hours, x, of the snowstorm, and the number of inches of snow, y, on the ground?

To find the equation that models the relationship between the number of hours (\(x\)) of the snowstorm and the number of inches of snow (\(y\)) on the ground, we can use the two points given: (0, 3) and (5, 18).

1. **Determine the slope \(m\)** using the formula:
   \[
   m = \frac{y_2 - y_1}{x_2 - x_1}
   \]
   Substituting in the points:
   \[
   m = \frac{18 - 3}{5 - 0} = \frac{15}{5} = 3
   \]

2. **Use the point-slope form of the equation**:
   \[
   y - y_1 = m(x - x_1)
   \]
   Using the point (0, 3):
   \[
   y - 3 = 3(x - 0)
   \]
   Simplifying this gives:
   \[
   y = 3x + 3
   \]

Thus, the equation that models the relationship is:
\[
y = 3x + 3
\]

Would you like to explore more details or have any questions? Here are some related questions to consider:

1. How do you find the y-intercept of a linear equation?
2. What is the significance of the slope in this context?
3. How can you interpret the graph of this equation?
4. What would the equation look like if the snow fell at a different rate?
5. Can you describe how to verify this equation with additional data points? 

**Tip:** Always plot additional points to ensure your equation accurately represents the data.

During a snowstorm, snow falls at a constant rate and is recorded by a meteorologist. The data is plotted on the graph below. Which equation models the relationship between the number of hours, x, of the snowstorm, and the number of inches of snow, y, on the ground?

Explore how to model the relationship between hours of a snowstorm and inches of snow using linear equations. The problem involves key concepts like slope and intercept, leading to the equation y = 3x + 3, based on data points (0, 3) and (5, 18). Suitable for students in Grades 6-8.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation