Math Problem Statement

y=-2x-5

Solution

The equation given is:

y=2x5y = -2x - 5

This represents a linear equation in slope-intercept form:

y=mx+by = mx + b

where:

  • m=2m = -2 (the slope)
  • b=5b = -5 (the y-intercept)

Key Properties:

  1. Slope: 2-2 means the line decreases by 2 units for every 1 unit increase in xx.
  2. Y-Intercept: The graph crosses the yy-axis at (0,5)(0, -5).
  3. X-Intercept: Setting y=0y = 0 to find where the graph crosses the xx-axis: 0=2x50 = -2x - 5 2x=52x = -5 x=52x = -\frac{5}{2} So, the x-intercept is (52,0)\left(-\frac{5}{2}, 0\right).
  4. Graph Behavior: The line slopes downward from left to right due to the negative slope.
  5. Parallel and Perpendicular Lines:
    • Any line with the same slope (m=2m = -2) is parallel.
    • A perpendicular line will have a slope of 12\frac{1}{2} (the negative reciprocal of 2-2).

Would you like a graph or further clarification?

Related Questions:

  1. What is the equation of a line parallel to y=2x5y = -2x - 5 passing through (3,4)(3,4)?
  2. How do you convert this equation into standard form Ax+By=CAx + By = C?
  3. What is the equation of a line perpendicular to y=2x5y = -2x - 5 passing through (1,2)(-1,2)?
  4. How do you determine the distance from a point (e.g., (1,1)(1,1)) to this line?
  5. How does changing the slope affect the steepness of the line?

Tip:

For any linear equation in the form y=mx+by = mx + b, the slope determines the direction and steepness, while the y-intercept tells you where the line crosses the y-axis.

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Math Problem Analysis

Mathematical Concepts

Linear Equations
Slope-Intercept Form
Algebra

Formulas

y = mx + b

Theorems

Slope-intercept form properties
Parallel and perpendicular lines

Suitable Grade Level

Grades 7-9