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.