Math Problem Statement

intercept ans zero

intercept ans zero

Solution

This graph depicts a line crossing both the x-axis and y-axis on a coordinate plane. Based on this, we can derive the following:

  1. X-intercept: This is the point where the line crosses the x-axis. In this case, the x-intercept is at (7,0)(7, 0), meaning the line crosses the x-axis at x=7x = 7.

  2. Y-intercept: This is the point where the line crosses the y-axis. In this case, the y-intercept is at (0,7)(0, -7), meaning the line crosses the y-axis at y=7y = -7.

  3. Zero of the Function: The x-intercept is also the zero of the function, which means that when y=0y = 0, the value of xx is 7. So the zero of the function is x=7x = 7.

Would you like further details on the slope of this line or how the intercepts were determined?

Here are 5 questions related to this topic:

  1. How can we calculate the slope of this line based on its intercepts?
  2. What is the equation of this line in slope-intercept form?
  3. How would the graph change if the y-intercept were positive?
  4. What happens to the x-intercept if the slope of the line is changed?
  5. How do you determine the slope if only given two points?

Tip: The slope of a line is calculated as the change in yy divided by the change in xx (rise over run).

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Math Problem Analysis

Mathematical Concepts

Coordinate Geometry
Linear Equations
Intercepts

Formulas

y = mx + b
Slope = (change in y) / (change in x)

Theorems

Slope-Intercept Theorem

Suitable Grade Level

Grades 8-10