https://file.aiquickdraw.com/mathbot/file/1730369916171xy39l7ku.jpg

To find the slope of the graph for the given equation:

\[
y = \frac{1}{3}(29x + 10) + 5x
\]

we should first simplify this expression by distributing and combining like terms.

1. Distribute \(\frac{1}{3}\) across \(29x + 10\):

   \[
   y = \frac{1}{3} \cdot 29x + \frac{1}{3} \cdot 10 + 5x
   \]

   Simplify each term:

   \[
   y = \frac{29}{3}x + \frac{10}{3} + 5x
   \]

2. Combine the terms with \(x\):

   \[
   y = \left(\frac{29}{3} + 5\right)x + \frac{10}{3}
   \]

   To add \(\frac{29}{3}\) and \(5\), convert \(5\) to a fraction with a denominator of 3:

   \[
   y = \left(\frac{29}{3} + \frac{15}{3}\right)x + \frac{10}{3}
   \]

   \[
   y = \frac{44}{3}x + \frac{10}{3}
   \]

3. Now, the equation is in slope-intercept form \(y = mx + b\), where \(m\) is the slope.

   Here, the slope \(m = \frac{44}{3}\).

### Answer:
The slope of the graph is \(\frac{44}{3}\).

Would you like further details or have any questions?

---

#### Related Questions:
1. How do we convert a linear equation to slope-intercept form?
2. What does the slope represent in the context of a graph?
3. How would the graph change if the slope were negative?
4. How can we verify the slope by plugging in two points?
5. How does distributing a fraction work in algebra?

#### Tip:
When combining like terms with fractions, it's helpful to convert integers to fractions for easy addition.

What is the slope of the graph of y = 1/3 (29x + 10) + 5x in the xy-plane?

Learn how to find the slope of the linear equation y = 1/3 (29x + 10) + 5x. This problem covers core algebraic concepts, including the distributive property and combining like terms. Suitable for students in Grades 9-10.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation