Math Problem Statement

What are the intercepts of y = 2x + 6?

Solution

To find the intercepts of the line given by the equation y=2x+6y = 2x + 6, let's determine both the x-intercept and y-intercept.

1. Finding the y-intercept

The y-intercept occurs when x=0x = 0.

y=2(0)+6=6y = 2(0) + 6 = 6

So, the y-intercept is at the point (0,6)(0, 6).

2. Finding the x-intercept

The x-intercept occurs when y=0y = 0.

0=2x+60 = 2x + 6

Solving for xx: 2x=62x = -6 x=3x = -3

So, the x-intercept is at the point (3,0)(-3, 0).

Conclusion

The intercepts are:

  • x-intercept: (3,0)(-3, 0)
  • y-intercept: (0,6)(0, 6)

The correct answer choice is:

  • A. The intercept(s) is/are (3,0)(-3, 0) and (0,6)(0, 6).

Would you like further details or have any questions?

Here are some related questions to explore further:

  1. How can you determine the slope of a line from its equation?
  2. What is the significance of the slope-intercept form y=mx+by = mx + b?
  3. How do intercepts change when you adjust the slope or intercept in an equation?
  4. What are the intercepts for a quadratic equation?
  5. 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

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Suitable Grade Level

Grades 7-9