Math Problem Statement
y=2x+3
Solution
The equation you provided, , represents a linear function. Let's analyze its key components:
1. Slope-Intercept Form
The equation is in slope-intercept form, , where:
- is the slope.
- is the y-intercept.
For :
- Slope (m):
- Y-Intercept (b):
2. Characteristics of the Line
- Slope: The slope of 2 means that for every 1 unit increase in , the value of increases by 2 units.
- Y-Intercept: The line crosses the y-axis at the point .
3. Graphing the Line
To graph this equation:
- Start by plotting the y-intercept (0, 3) on the coordinate plane.
- Use the slope to find another point. Since the slope is 2, move up 2 units and 1 unit to the right from the y-intercept to get the next point, (1, 5).
- Draw a straight line through these points.
4. Example Points on the Line
Here are a few points that satisfy the equation:
- (y-intercept)
Would you like a graph or further details?
Related Questions
- How do you find the slope and y-intercept from any linear equation?
- What is the meaning of a negative slope?
- How do you convert a linear equation from slope-intercept to standard form?
- How does changing the slope affect the graph of a line?
- What are parallel and perpendicular lines?
Tip: Understanding how to interpret the slope and y-intercept helps in quickly graphing and analyzing linear equations.
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Math Problem Analysis
Mathematical Concepts
Algebra
Linear Equations
Slope-Intercept Form
Formulas
y = mx + b (Slope-Intercept Form)
Theorems
Slope-Intercept Theorem
Suitable Grade Level
Grades 7-8