Math Problem Statement
y=-2x-5
Solution
The equation given is:
This represents a linear equation in slope-intercept form:
where:
- (the slope)
- (the y-intercept)
Key Properties:
- Slope: means the line decreases by 2 units for every 1 unit increase in .
- Y-Intercept: The graph crosses the -axis at .
- X-Intercept: Setting to find where the graph crosses the -axis: So, the x-intercept is .
- Graph Behavior: The line slopes downward from left to right due to the negative slope.
- Parallel and Perpendicular Lines:
- Any line with the same slope () is parallel.
- A perpendicular line will have a slope of (the negative reciprocal of ).
Would you like a graph or further clarification?
Related Questions:
- What is the equation of a line parallel to passing through ?
- How do you convert this equation into standard form ?
- What is the equation of a line perpendicular to passing through ?
- How do you determine the distance from a point (e.g., ) to this line?
- How does changing the slope affect the steepness of the line?
Tip:
For any linear equation in the form , the slope determines the direction and steepness, while the y-intercept tells you where the line crosses the y-axis.
Ask a new question for Free
By Image
Drop file here or Click Here to upload
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