Math Problem Statement
Solution
Let's go through the graph to answer the questions.
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y-intercept: This is the point where the line crosses the y-axis. From the graph, the line crosses the y-axis at .
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Slope: To calculate the slope , we use the formula: From the graph, two points on the line are and . So: Therefore, the slope is .
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Equation of the line in slope-intercept form: The slope-intercept form of a line is: where is the slope and is the y-intercept. With and , the equation becomes:
So the answers are:
- y-intercept:
- slope:
- equation of the line:
Would you like more details on any part of this?
Here are 5 related questions to deepen your understanding:
- How do you find the y-intercept if the graph isn't provided but you're given the equation?
- What happens to the slope if the line is steeper or flatter?
- Can you explain what the slope of 0 means in the context of a graph?
- How would you find the x-intercept of the line from the given equation?
- How can you use the slope formula to check if three points are collinear?
Tip: When calculating slope from a graph, always double-check the rise and run between two distinct points on the line to avoid calculation mistakes.
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Math Problem Analysis
Mathematical Concepts
Algebra
Coordinate Geometry
Linear Equations
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