Math Problem Statement

Determina los puntos de intersección de la recta con los ejes coordenados. Intersección con el eje x: ( ); Intersección con el eje y: ( ).

Solution

The problem requires determining the intersection points of the line with the x-axis and y-axis.

Let's solve it step-by-step:

  1. Intersection with the x-axis:

    • At the x-axis, y=0y = 0.
    • We observe from the graph that the line crosses the x-axis at approximately x=5x = 5.
    • Thus, the point of intersection with the x-axis is (5,0)(5, 0).
  2. Intersection with the y-axis:

    • At the y-axis, x=0x = 0.
    • From the graph, the line crosses the y-axis at approximately y=7y = -7.
    • Therefore, the point of intersection with the y-axis is (0,7)(0, -7).

Final answers:

  • Intersection with the x-axis: (5,0)(5, 0).
  • Intersection with the y-axis: (0,7)(0, -7).

Do you have any questions or would you like more details on how these points were determined?

Here are five related questions you could explore:

  1. What is the equation of the line in slope-intercept form?
  2. How do you determine the slope of the line from the graph?
  3. Can you find the midpoint between the intersection points on the x-axis and y-axis?
  4. What happens to the intersection points if the slope of the line changes?
  5. How would the intersection points change if the line had a negative slope?

Tip: To find the slope of a line, use the formula m=ΔyΔxm = \frac{\Delta y}{\Delta x} where Δy\Delta y and Δx\Delta x are the changes in the y and x values between two points on the line.

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Math Problem Analysis

Mathematical Concepts

Linear Equations
Graphing

Formulas

Slope-intercept form y = mx + b

Theorems

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Suitable Grade Level

Grades 7-10