Math Problem Statement

Consider the graph of y = x - 2. State the coordinates of the x-intercept.

Solution

The graph provided represents the line given by the equation y=x2y = x - 2. To solve part 4a, we need to determine the x-intercept, where the line crosses the x-axis.

To find the x-intercept:

  1. Set y=0y = 0 because the y-value at the x-intercept is always zero.
  2. Solve for xx.

Step-by-Step Solution:

Starting with the equation: y=x2y = x - 2 Set y=0y = 0: 0=x20 = x - 2 Solve for xx: x=2x = 2

Thus, the coordinates of the x-intercept are (2,0)(2, 0).

Would you like more details or have any other questions?

Here are 5 related questions for practice:

  1. What is the y-intercept of the line y=x2y = x - 2?
  2. How would the graph change if the equation were y=x+3y = x + 3?
  3. Find the slope of the line y=x2y = x - 2 and explain its significance.
  4. How do you find the point where two lines intersect?
  5. What is the distance between the origin and the x-intercept of y=x2y = x - 2?

Tip: The slope-intercept form of a line is 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

Algebra
Linear Equations
Coordinate Geometry

Formulas

y = mx + b

Theorems

X-intercept of a line (set y = 0)

Suitable Grade Level

Grades 7-9