Blue Paint (cups) 1 Red Paint (cups) 1.5 3 2 Here is your table from the previous screen. Write an equation for the relationship between the number cups of blue paint, b, and the number of cups of red paint, r. 4.67 10 7 15

We have two variables: 
- \( b \): the number of cups of blue paint
- \( r \): the number of cups of red paint

The table seems to provide pairs of values for \( b \) (blue paint) and \( r \) (red paint), and we want to find an equation that expresses the relationship between them.

Given the values:

\[
\begin{array}{|c|c|}
\hline
\text{Blue Paint } (b) & \text{Red Paint } (r) \\
\hline
1 & 1.5 \\
3 & 2 \\
4.67 & 10 \\
7 & 15 \\
\hline
\end{array}
\]

### Step 1: Determine the relationship between \( b \) and \( r \)
We want to determine if there is a linear relationship between \( b \) and \( r \), which could be expressed in the form:

\[
r = m \cdot b + c
\]

Where \( m \) is the slope, and \( c \) is the y-intercept. We can use two points from the table to calculate the slope.

Using the points \( (1, 1.5) \) and \( (3, 2) \):

\[
m = \frac{r_2 - r_1}{b_2 - b_1} = \frac{2 - 1.5}{3 - 1} = \frac{0.5}{2} = 0.25
\]

So, the slope \( m \) is 0.25.

### Step 2: Calculate the intercept
Now, substitute one point into the equation to solve for \( c \). Using \( (1, 1.5) \):

\[
1.5 = 0.25(1) + c
\]
\[
c = 1.5 - 0.25 = 1.25
\]

### Step 3: Write the equation
The equation relating \( r \) (red paint) to \( b \) (blue paint) is:

\[
r = 0.25b + 1.25
\]

Would you like further details or have any questions about this process?

### Related questions:
1. What happens to the amount of red paint if the amount of blue paint doubles?
2. How does the slope affect the relationship between the paints?
3. Can the relationship be non-linear in other contexts? How would you find out?
4. How would you interpret the y-intercept of 1.25 in a real-world scenario?
5. If \( b = 6 \), what would be the corresponding value of \( r \)?

**Tip:** Always double-check your slope calculation by testing more than one pair of points.

Discover how to derive the linear equation that represents the relationship between the number of cups of blue paint and red paint. Using the slope-intercept form and data from the table, the solution includes key algebraic concepts. Suitable for 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