Math Problem Statement
Reduce the following line slope interest form and intersect form (a) 2x+3y-6=0
Solution
To reduce the given equation into slope-intercept form () and standard intercept form (), follow these steps:
1. Slope-Intercept Form ():
The general slope-intercept form of a line is:
Start with the given equation:
Rearrange to isolate :
Divide through by 3:
Here:
- Slope () =
- Y-intercept () = 2
2. Intercept Form ():
The general intercept form of a line is:
Start with the given equation:
Solve for the intercept form:
Divide through by 6 to normalize:
Simplify the fractions:
Here:
- X-intercept () =
- Y-intercept () =
Final Results:
-
Slope-Intercept Form:
-
Intercept Form:
Would you like a detailed plot or further clarifications?
Expanding Questions:
- How can the slope be interpreted geometrically in the graph of a line?
- What happens to the intercepts if the equation coefficients change?
- How would you convert intercept form back to slope-intercept form?
- What is the geometric significance of having one intercept at zero?
- How do parallel and perpendicular lines relate to the slope of this line?
Tip: Always ensure the line equation is simplified before extracting slope or intercepts to avoid calculation errors.
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Math Problem Analysis
Mathematical Concepts
Algebra
Linear Equations
Slope-Intercept Form
Intercept Form
Formulas
Slope-Intercept Form: y = mx + b
Intercept Form: x/a + y/b = 1
Theorems
Properties of Linear Equations
Suitable Grade Level
Grades 8-10