The function \( q(t) = \frac{2t + 7}{3} \) represents a linear function of \( t \), divided by 3.

We can express it in different forms:

\[
q(t) = \frac{2t}{3} + \frac{7}{3}
\]

This form separates the terms so that it's clearer how \( t \) and the constant are affected by division. The slope of the function is \( \frac{2}{3} \) and the y-intercept is \( \frac{7}{3} \).

Would you like a more detailed breakdown of the steps involved, or do you have any specific questions about the function?

Here are some related questions to consider:
1. What is the slope of the function, and how does it influence the graph?
2. How would you graph this function on a coordinate plane?
3. How does the y-intercept affect the placement of the line on the graph?
4. What happens if you change the coefficient of \( t \) or the constant in the function?
5. Can you rewrite the function in a different form, such as using function notation?

**Tip:** In any linear function of the form \( q(t) = mt + b \), \( m \) is the slope and \( b \) is the y-intercept. These parameters define the steepness and the position of the line on the graph.

Explore the linear function q(t) = (2t + 7) / 3 with a breakdown of the slope, y-intercept, and how the function behaves. Learn key algebraic concepts such as slope-intercept form, graphing linear functions, and how changing the coefficients affects the graph. 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