Math Problem Statement

The equation of a line is y = 2x + 10. What is the y-intercept of the line?

Solution

The equation given is y=2x+10y = 2x + 10. This equation is in slope-intercept form, y=mx+by = mx + b, where:

  • mm represents the slope of the line.
  • bb represents the yy-intercept.

The yy-intercept is the value of yy when x=0x = 0. From the equation y=2x+10y = 2x + 10, we can see that b=10b = 10.

Thus, the yy-intercept of the line is 1010, which corresponds to the point (0,10)(0, 10).

Would you like more details or have any questions? Here are five related questions to expand your understanding:

  1. How do you calculate the slope of a line from its equation?
  2. What does the slope represent in the context of this equation?
  3. Can the yy-intercept change if the slope or another part of the equation changes?
  4. How do you find the xx-intercept of a line given its equation?
  5. Can a line have more than one yy-intercept? Why or why not?

Tip: Always remember that the yy-intercept is the constant term in the slope-intercept form y=mx+by = mx + b.

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Math Problem Analysis

Mathematical Concepts

Algebra
Linear Equations
Slope-Intercept Form

Formulas

Slope-intercept form: y = mx + b

Theorems

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Suitable Grade Level

Grades 6-8