Math Problem Statement

On this grid, draw the line y = x.

Solution

The problem requires drawing the line y=xy = x on the grid provided.

To draw the line y=xy = x:

  1. Note that y=xy = x is a linear equation with a slope of 11 and a y-intercept of 00.
  2. This line passes through the origin, (0,0)(0, 0), and follows a path where for every unit increase in xx, yy increases by the same amount.
  3. Plot points where y=xy = x, such as (1,1)(1, 1), (2,2)(2, 2), (3,3)(3, 3), (1,1)(-1, -1), (2,2)(-2, -2), and (3,3)(-3, -3).
  4. Connect these points to create a straight line extending diagonally from the bottom-left to the top-right of the grid.

The result should be a line passing through points (0,0)(0, 0), (1,1)(1, 1), (2,2)(2, 2), etc., forming a 45-degree angle with both axes.

Would you like additional details on this solution?


Here are 5 follow-up questions that might deepen your understanding:

  1. What is the slope of the line y=xy = x and how does it affect the line's orientation?
  2. How would the line look if the equation were y=xy = -x?
  3. What are the key differences between the lines y=xy = x and y=x+1y = x + 1?
  4. How would you draw the line y=2xy = 2x on the same grid?
  5. What points would you plot for the line y=12xy = \frac{1}{2}x?

Tip: For any line y=mx+by = mx + b, mm represents the slope (rise over run), and bb is the y-intercept (where the line crosses the y-axis).

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Math Problem Analysis

Mathematical Concepts

Linear Equations
Graphing
Coordinate Geometry

Formulas

y = mx + b (slope-intercept form)

Theorems

Slope of a line
Intercept theorem

Suitable Grade Level

Grades 7-9