https://file.aiquickdraw.com/mathbot/file/17261486904846x0mq1i4.jpg

You have provided a photo containing a mathematical problem. Let's address each part of the question as seen in the image:

### The Equation and Table Filling:
The equation provided is:
\[ y = 1 + \frac{5}{3}x \]

You need to find the \( y \)-coordinate for each given value of \( x \). The table appears to have \( x \) values from 0 to 2. Let's calculate the corresponding \( y \) values:

- For \( x = 0 \):
  \[ y = 1 + \frac{5}{3} \times 0 = 1 \]

- For \( x = 1 \):
  \[ y = 1 + \frac{5}{3} \times 1 = 1 + \frac{5}{3} = \frac{8}{3} \]

- For \( x = 2 \):
  \[ y = 1 + \frac{5}{3} \times 2 = 1 + \frac{10}{3} = \frac{13}{3} \]

### Initial Function Value:
The initial value of the function when \( x = 0 \) is \( y = 1 \).

### Change in \( y \) for Each Unit Increase in \( x \):
The function \( y = 1 + \frac{5}{3}x \) has a slope of \( \frac{5}{3} \), indicating that the \( y \)-value changes by \( \frac{5}{3} \) for each 1-unit increase in the \( x \)-value.

If you have more questions or need further explanations on any of these calculations, feel free to ask!

### Further Questions:
1. Would you like to know how to graph this equation?
2. Do you need to solve for \( x \) given a specific \( y \) value?
3. Are you interested in understanding the implications of the slope and the y-intercept in this context?
4. Would you like a walkthrough on how to derive this equation from two given points?
5. Need help with a different type of linear equation problem?

### Tip:
Remember that in linear equations of the form \( y = mx + b \), \( m \) represents the slope (rate of change of \( y \) with respect to \( x \)), and \( b \) represents the y-intercept (the value of \( y \) when \( x = 0 \)).

For the equation, y = 1 + 5/3x, find the y-coordinate for each value of x. If needed, write any answer as a reduced fraction.

Learn how to solve the linear equation y = 1 + 5/3x by calculating the y-values for given x-values. Understand how the slope and intercept work in this equation. This problem is suitable for students in Grades 8-10.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation