Math Problem Statement
2x+5y=15
Solution
The equation 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 in terms of : Or solve for in terms of :
2. Finding intercepts:
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x-intercept: Set , then solve for : So, the x-intercept is .
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y-intercept: Set , then solve for : So, the y-intercept is .
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 , where is the slope and is the y-intercept: Here, the slope and the y-intercept is .
5. Standard form:
This equation is already in standard form , where , , and .
Do you want more details on any of these methods, or have any other questions?
Here are 5 related questions:
- How can we solve this system if we add another equation?
- How do you determine the slope of a line from its equation?
- How can we graph this linear equation step by step?
- Can we find a specific solution for and given additional constraints?
- 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.
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Math Problem Analysis
Mathematical Concepts
Linear Equations
Algebra
Formulas
2x + 5y = 15
y = (15 - 2x) / 5
x = (15 - 5y) / 2
Slope-Intercept Form: y = mx + b
Standard Form: Ax + By = C
Theorems
Slope-Intercept Theorem
Suitable Grade Level
Grades 6-9