Math Problem Statement
Solution
To find the equation of the linear function whose graph is shown, we need to determine two key elements:
- Slope (m): This measures the steepness and direction of the line.
- Y-intercept (b): This is the point where the line crosses the y-axis.
Step 1: Identify Two Points on the Line
From the graph, we can identify two points:
- Point A: (2, 7)
- Point B: (-3, -2)
Step 2: Calculate the Slope (m)
The slope formula is: Using the points (2, 7) and (-3, -2): The slope .
Step 3: Find the Y-intercept (b)
We use the slope-intercept form of the equation: Substitute one of the points into the equation. Using point (2, 7): Subtract from both sides to solve for :
Final Equation
The equation of the line is:
Would you like further details or have any questions?
Here are five related questions to expand your understanding:
- How would the equation change if the slope was negative?
- What does the y-intercept tell you about the graph of the line?
- Can you find the x-intercept for this equation?
- How would you write the equation in standard form ?
- How do you find the slope if you know the angle of the line?
Tip: Always check the signs of your slope and y-intercept carefully; they indicate the direction and position of the line on the graph.
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Math Problem Analysis
Mathematical Concepts
Linear Equations
Slope-Intercept Form
Formulas
Slope Formula m = (y2 - y1) / (x2 - x1)
Slope-Intercept Form y = mx + b
Theorems
Linear Equation Theorem
Suitable Grade Level
Grades 8-10
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