https://file.aiquickdraw.com/mathbot/file/1726776596136zpqh8vmk.jpg

Let's analyze the linear equation \( y = \frac{3}{4}x - 6 \) and identify the features requested:

1. **Slope**: The equation is in slope-intercept form \( y = mx + b \), where \( m \) is the slope. Here, \( m = \frac{3}{4} \), so the slope is \( \frac{3}{4} \).

2. **y-intercept**: The y-intercept is the value of \( y \) when \( x = 0 \). From the equation, when \( x = 0 \), \( y = -6 \). So, the y-intercept is \( -6 \).

3. **x-intercept**: To find the x-intercept, set \( y = 0 \) and solve for \( x \):
   \[
   0 = \frac{3}{4}x - 6
   \]
   \[
   \frac{3}{4}x = 6
   \]
   \[
   x = 6 \times \frac{4}{3} = 8
   \]
   So, the x-intercept is \( 8 \).

4. **Zero of the function**: The zero of the function is the same as the x-intercept, which is \( 8 \).

### Summary of features:
- Slope: \( \frac{3}{4} \)
- y-intercept: \( -6 \)
- x-intercept: \( 8 \)
- Zero of the function: \( 8 \)

Would you like further clarification or a more detailed explanation on any of these points?

Here are 5 related questions to expand your understanding:
1. How do you determine the slope from a linear equation in other forms?
2. What happens to the graph if the y-intercept changes?
3. How can you quickly find the x-intercept using a graph?
4. How does the slope affect the steepness of the line?
5. Can a linear equation have more than one x-intercept?

**Tip**: Always set \( y = 0 \) to find the x-intercept and \( x = 0 \) to find the y-intercept when dealing with linear equations!

Graph the equation y = (3/4)x - 6 on the coordinate plane and identify its slope, y-intercept, x-intercept, and the zero of the function.

Learn how to graph the linear equation y = (3/4)x - 6, and determine its slope, y-intercept, x-intercept, and zero of the function. This example uses the slope-intercept form and highlights key linear function properties.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation