Math Problem Statement

In the following exercises, find the x- and y-intercepts on each graph.

Solution

In the provided graphs, we need to find the x- and y-intercepts. The x-intercept is where the line crosses the x-axis (i.e., where y=0y = 0), and the y-intercept is where the line crosses the y-axis (i.e., where x=0x = 0).

Problem 33:

  • X-intercept: The line crosses the x-axis at x=3x = 3.
  • Y-intercept: The line crosses the y-axis at y=3y = 3.

Problem 34:

  • X-intercept: The line crosses the x-axis at x=4x = 4.
  • Y-intercept: The line crosses the y-axis at y=2y = -2.

Problem 35:

  • X-intercept: The line crosses the x-axis at x=5x = 5.
  • Y-intercept: The line crosses the y-axis at y=5y = -5.

Problem 36:

  • X-intercept: The line crosses the x-axis at x=2x = -2.
  • Y-intercept: The line crosses the y-axis at y=6y = 6.

Would you like a further breakdown or have additional questions?

Here are five relative questions to expand the topic:

  1. How do we find the equation of the line from the intercepts?
  2. Can you explain how the slope relates to the intercepts in these graphs?
  3. What is the slope of the line in each graph?
  4. How would the intercepts change if we adjusted the slope of the line?
  5. How do we interpret these intercepts in real-world contexts?

Tip: The formula for a line is often expressed as y=mx+by = mx + b, where mm is the slope and bb is the y-intercept.

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Math Problem Analysis

Mathematical Concepts

Coordinate Geometry
Intercepts

Formulas

y = mx + b
x-intercept (y = 0)
y-intercept (x = 0)

Theorems

Linear Equation Theorem

Suitable Grade Level

Grades 8-10