The equation given is \( 2x + 4y = 5 \).

This is a linear equation in two variables \( x \) and \( y \). Let's analyze it further:

### 1. **Slope-Intercept Form**
We can rearrange the equation into the slope-intercept form, \( y = mx + c \), where \( m \) is the slope and \( c \) is the y-intercept.

\[
2x + 4y = 5
\]

To solve for \( y \), subtract \( 2x \) from both sides:

\[
4y = -2x + 5
\]

Now, divide by 4:

\[
y = -\frac{2}{4}x + \frac{5}{4}
\]

Simplifying further:

\[
y = -\frac{1}{2}x + \frac{5}{4}
\]

Here, the slope \( m = -\frac{1}{2} \) and the y-intercept \( c = \frac{5}{4} \).

### 2. **Intercepts**
- **x-intercept:** Set \( y = 0 \) and solve for \( x \):
  \[
  2x + 4(0) = 5 \quad \Rightarrow \quad x = \frac{5}{2}
  \]
  So, the x-intercept is \( \left(\frac{5}{2}, 0\right) \).

- **y-intercept:** Set \( x = 0 \) and solve for \( y \):
  \[
  2(0) + 4y = 5 \quad \Rightarrow \quad y = \frac{5}{4}
  \]
  So, the y-intercept is \( \left(0, \frac{5}{4}\right) \).

### 3. **Graphical Interpretation**
The equation represents a straight line on the Cartesian plane, with a slope of \( -\frac{1}{2} \). It decreases from left to right.

Would you like a graphical representation or any other details?

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Here are 5 related questions you might find interesting:

1. What is the significance of the slope in the context of this equation?
2. How do you find the distance between the origin and the line \( 2x + 4y = 5 \)?
3. What happens if we set \( y = 1 \) in the equation? What is the corresponding \( x \) value?
4. How would you solve this equation if an additional constraint \( x > 0 \) was applied?
5. Can this equation represent a real-world scenario? If so, what might that be?

**Tip:** When finding the slope-intercept form of a line, make sure to express \( y \) in terms of \( x \) to easily identify the slope and y-intercept.

Learn how to solve the linear equation 2x + 4y = 5 with a detailed step-by-step solution. This problem covers key algebraic concepts, including linear equations and the slope-intercept form. Suitable for students in Grades 7-9.

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