Math Problem Statement
Determine the equations of the three given lines based on their graphs.
Solution
To find the equations of the lines shown in each graph, we can use the slope-intercept form of a line, , where is the slope and is the y-intercept.
First graph:
- Y-intercept: The line crosses the y-axis at , so .
- Slope: The slope is calculated as . From one point (e.g., ) to another (e.g., ), the rise is and the run is . Therefore, the slope is .
- Equation: .
Second graph:
- Y-intercept: The line crosses the y-axis at , so .
- Slope: Using the points and , the rise is and the run is , so the slope is .
- Equation: .
Third graph:
- Y-intercept: The line crosses the y-axis at , so .
- Slope: Using the points and , the rise is and the run is , so the slope is .
- Equation: .
Would you like a more detailed explanation or have any other questions?
Here are some related questions you might explore:
- What happens when the slope is zero?
- How does changing the y-intercept affect the graph of the line?
- How can you derive the slope if only two points are given?
- Can you determine the slope if the line is vertical or horizontal?
- How would you graph a line given its equation in point-slope form?
Tip: Remember, the slope describes the steepness of a line. A negative slope means the line is falling, while a positive slope means it's rising.
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Math Problem Analysis
Mathematical Concepts
Algebra
Linear Equations
Graphing
Formulas
Slope-intercept form: y = mx + b
Slope formula: m = (y2 - y1) / (x2 - x1)
Theorems
Slope-intercept form of a line
Suitable Grade Level
Grades 8-10