Math Problem Statement
Solution
To determine the equation of the line in slope-intercept form, , let's analyze the line on the graph.
Step 1: Identify the Slope ()
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Choose two points on the line. From the image, we can see two clear points at:
- Point 1:
- Point 2:
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Calculate the slope using the formula: Plugging in the values:
Step 2: Identify the Y-Intercept ()
From the graph, the line crosses the y-axis at . Therefore, the y-intercept is 6.
Step 3: Write the Equation
Now that we have the slope and the y-intercept , the equation of the line is:
Would you like a detailed explanation of each step, or do you have any questions?
Here are some related questions for practice:
- How would you find the equation if the slope was positive instead?
- What would change in the equation if the y-intercept was negative?
- How do you find the slope if the coordinates are decimals instead of integers?
- How would you rewrite the equation in standard form?
- How do you interpret the slope of a line in real-life contexts?
Tip: Always ensure you double-check the slope and intercept points directly on the graph to avoid any small errors.
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Math Problem Analysis
Mathematical Concepts
Algebra
Linear Equations
Slope-Intercept Form
Formulas
Slope formula: m = (y2 - y1) / (x2 - x1)
Slope-intercept form: y = mx + b
Theorems
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Suitable Grade Level
Grades 8-10