The equation $2x + 5y = 15$ represents a linear equation in two variables. There are various ways to approach or analyze this equation, depending on what you want to do with it. Here are a few possibilities:

1. Solving for one variable in terms of the other:

You can express one variable in terms of the other. For instance, solve for $y$ in terms of $x$: $5y = 15 - 2x$ $y = \frac{15 - 2x}{5}$ Or solve for $x$ in terms of $y$: $2x = 15 - 5y$ $x = \frac{15 - 5y}{2}$

2. Finding intercepts:

• x-intercept: Set $y = 0$, then solve for $x$: $2x = 15 \quad \Rightarrow \quad x = \frac{15}{2}$ So, the x-intercept is $\left( \frac{15}{2}, 0 \right)$.

• y-intercept: Set $x = 0$, then solve for $y$: $5y = 15 \quad \Rightarrow \quad y = 3$ So, the y-intercept is $(0, 3)$.

3. Graphing the equation:

You can plot the equation by finding two points (like the intercepts) and then drawing a line through them.

4. Slope-intercept form:

The equation can be rewritten in slope-intercept form $y = mx + b$, where $m$ is the slope and $b$ is the y-intercept: $y = -\frac{2}{5}x + 3$ Here, the slope $m = -\frac{2}{5}$ and the y-intercept is $3$.

5. Standard form:

This equation is already in standard form $Ax + By = C$, where $A = 2$, $B = 5$, and $C = 15$.

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Do you want more details on any of these methods, or have any other questions?

Here are 5 related questions:

1. How can we solve this system if we add another equation?
2. How do you determine the slope of a line from its equation?
3. How can we graph this linear equation step by step?
4. Can we find a specific solution for $x$ and $y$ given additional constraints?
5. What real-world situations can this equation represent?

Tip: In linear equations, the slope tells you how steep the line is, while the intercepts show where the line crosses the axes.