Math Problem Statement
What are the intercepts of y = 2x + 6?
Solution
To find the intercepts of the line given by the equation , let's determine both the x-intercept and y-intercept.
1. Finding the y-intercept
The y-intercept occurs when .
So, the y-intercept is at the point .
2. Finding the x-intercept
The x-intercept occurs when .
Solving for :
So, the x-intercept is at the point .
Conclusion
The intercepts are:
- x-intercept:
- y-intercept:
The correct answer choice is:
- A. The intercept(s) is/are and .
Would you like further details or have any questions?
Here are some related questions to explore further:
- How can you determine the slope of a line from its equation?
- What is the significance of the slope-intercept form ?
- How do intercepts change when you adjust the slope or intercept in an equation?
- What are the intercepts for a quadratic equation?
- How do intercepts help in graphing a line?
Tip: To find intercepts, set one variable to zero and solve for the other. This gives you the points where the line crosses the axes.
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Math Problem Analysis
Mathematical Concepts
Linear Equations
Intercepts
Formulas
y = mx + b
Theorems
-
Suitable Grade Level
Grades 7-9