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To find the equation that describes the relationship between gallons of white paint (\( x \)) and gallons of red paint (\( y \)) from the graph, we can analyze the slope.

The graph shows a line with two clear points:
- When \( x = 0 \) (white paint), \( y = 0 \) (red paint).
- When \( x = 5 \), \( y = 2 \).

### Step 1: Calculate the Slope
The slope \( m \) is calculated by the formula:
\[
m = \frac{\Delta y}{\Delta x} = \frac{y_2 - y_1}{x_2 - x_1}
\]
Using the points \((0, 0)\) and \((5, 2)\):
\[
m = \frac{2 - 0}{5 - 0} = \frac{2}{5}
\]

### Step 2: Write the Equation
Since the line passes through the origin \((0,0)\), the equation is of the form:
\[
y = mx
\]
Substituting the slope:
\[
y = \frac{2}{5}x
\]

### Final Answer
The equation that describes the relationship is:
\[
y = \frac{2}{5}x
\]

Would you like a more detailed explanation, or do you have any questions?

### Related Questions
1. How do you interpret the slope in terms of paint mixing ratios?
2. What would the equation look like if Jess needed more red paint for each gallon of white paint?
3. How would you graph this equation if given only the equation form?
4. What does it mean if the slope were negative in this context?
5. How would the equation change if the graph had a y-intercept other than zero?

### Tip:
When interpreting a graph, the slope can often reveal a ratio or rate of change between two variables, which is useful in real-world applications like mixing materials.

The graph relates the number of gallons of white paint to the number of gallons of red paint Jess used to make the perfect pink. Write an equation that describes the relationship.

Learn how to determine the linear equation for paint mixing ratios. This problem explores the relationship between gallons of white paint and red paint to create a specific color mix, using the slope-intercept form. Ideal for students in Grades 6-8.

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