Math Problem Statement
Graph the following features:
- Slope = 2
- Y-intercept = -2
Solution
The image asks for a graph of a line with the given features:
- Slope: 2
- Y-intercept: -2
Step-by-Step Solution:
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Identify the equation of the line:
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The slope-intercept form of a line is given by: where is the slope and is the y-intercept.
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For the given features:
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Plot the y-intercept:
- The y-intercept is -2. This is the point where the line crosses the y-axis. Plot this point at (0, -2) on the graph.
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Use the slope to find another point:
- The slope is 2, which can be interpreted as a rise of 2 units for every run of 1 unit.
- From the point (0, -2), move up 2 units and to the right 1 unit. This lands on the point (1, 0).
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Draw the line:
- Draw a straight line passing through the points (0, -2) and (1, 0). Extend the line in both directions.
Would you like me to generate an image of the graph or explain any other details?
Related Questions:
- What is the general form of the equation of a line?
- How do you convert a line from slope-intercept form to standard form?
- How does the slope of a line affect its steepness?
- What is the significance of the y-intercept in a graph?
- How can we find the x-intercept of a line given its equation?
Tip: When graphing lines, always start with the y-intercept and then use the slope to find additional points.
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Math Problem Analysis
Mathematical Concepts
Linear Equations
Graphing
Slope-Intercept Form
Formulas
Slope-intercept form: y = mx + b
Theorems
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Suitable Grade Level
Grades 6-8