Math Problem Statement
2x+5y=-5 Find the slope and the y-intercept. Then use them to graph the line.
Solution
We start with the given equation:
Step 1: Convert to Slope-Intercept Form ()
The slope-intercept form is:
where:
- is the slope
- is the y-intercept
Solve for :
Step 2: Identify the Slope and Y-Intercept
From the equation:
- Slope () =
- Y-Intercept () = (which corresponds to the point )
Step 3: Graphing the Line
- Plot the Y-Intercept: Start by plotting the point .
- Use the Slope: The slope means:
- Move down 2 units (negative direction).
- Move right 5 units (positive direction).
- Plot this second point.
- Draw the Line: Connect the points with a straight line extending in both directions.
Would you like a visual graph? Let me know!
Related Questions:
- How do you find the x-intercept of this equation?
- What happens to the graph if the equation changes to ?
- How can you verify the slope using two points on the line?
- What does a positive slope indicate compared to a negative slope?
- How do you determine if two lines are parallel?
Tip:
To check if a point is on the line, substitute its and values into the equation. If both sides are equal, the point lies on the line.
Ask a new question for Free
By Image
Drop file here or Click Here to upload
Math Problem Analysis
Mathematical Concepts
Algebra
Linear Equations
Slope-Intercept Form
Formulas
Slope-intercept form: y = mx + b
Slope formula: m = -A/B (from Ax + By = C)
Theorems
Equation of a straight line
Suitable Grade Level
Grades 7-9