Math Problem Statement

Y = -x + 3

Solution

The equation you provided is Y=x+3Y = -x + 3, which represents a straight line in the slope-intercept form Y=mx+bY = mx + b, where:

  • mm (the slope) is -1.
  • bb (the y-intercept) is 3.

Key Details:

  • Slope (m): The slope of the line is -1. This means the line decreases by 1 unit for every 1 unit increase in xx.
  • Y-intercept (b): The line crosses the y-axis at the point (0, 3).

Graphing:

  • When x=0x = 0, Y=3Y = 3.
  • When x=1x = 1, Y=1+3=2Y = -1 + 3 = 2.
  • When x=1x = -1, Y=1+3=4Y = 1 + 3 = 4.

If you plot these points, the line would slope downwards from left to right due to the negative slope.

Would you like more details or have any questions?

Here are 5 related questions for deeper understanding:

  1. What is the x-intercept of this line?
  2. How would the graph look if the slope were positive instead?
  3. What happens to the line if the y-intercept changes?
  4. Can you calculate the equation of a line parallel to this one but passing through a different point?
  5. How do you find the distance between this line and a point not on the line?

Tip: For any linear equation in slope-intercept form, the slope tells you the steepness and direction of the line.

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Math Problem Analysis

Mathematical Concepts

Algebra
Linear Equations
Slope-Intercept Form

Formulas

Slope-intercept form: Y = mx + b

Theorems

Slope and Y-intercept relationship

Suitable Grade Level

Grades 8-10