Math Problem Statement
y = -2x+3
Solution
The equation is another linear equation in slope-intercept form, where:
- is the dependent variable.
- is the independent variable.
- The coefficient of , which is -2, represents the slope of the line.
- The constant term, 3, is the y-intercept.
Characteristics of the Line:
- Slope (m): The slope is -2, indicating that the line falls 2 units vertically for every 1 unit it moves horizontally to the right. This is a negative slope, so the line will slant downwards from left to right.
- Y-Intercept (b): The y-intercept is 3, meaning the line crosses the y-axis at the point (0, 3).
Graph of the Line:
To graph this equation:
- Start at the y-intercept (0, 3): Plot this point on the y-axis.
- Use the slope to find another point:
- From (0, 3), use the slope , which means go down 2 units and 1 unit to the right. This brings you to the point (1, 1).
- Draw the line: Draw a straight line through the points (0, 3) and (1, 1).
Graph Summary:
The line will pass through the y-axis at 3 and will descend at an angle due to the negative slope.
Would you like more details or have any questions?
Here are 5 related questions you might find interesting:
- How can you find the equation of a line given two points?
- What happens to the graph of a line if you change the slope?
- How do you determine the x-intercept of a line from its equation?
- What does a negative slope tell you about the direction of a line?
- How can you find the point of intersection between two linear equations?
Tip: For a negative slope, always remember that as you move to the right, the line will move downward.
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Math Problem Analysis
Mathematical Concepts
Linear Equations
Slope-Intercept Form
Formulas
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Theorems
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Suitable Grade Level
Grades 7-9