Math Problem Statement
Solution
The task asks to write a slope-intercept equation for a line that passes through the points (-7, 0) and (4, -2).
Steps to solve:
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Find the slope () of the line using the slope formula: Here, and .
Substituting the values: So, the slope is .
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Use the point-slope form of the equation to find the equation of the line: Using the point and the slope :
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Simplify to slope-intercept form (): Distribute the :
Thus, the slope-intercept form of the equation is:
Would you like a detailed explanation of any of the steps? Let me know!
Here are 5 questions that expand on the topic:
- How do you find the y-intercept from two points?
- Can you derive the slope-intercept form directly from the two points without using point-slope form?
- What does the slope of a line tell you about its direction and steepness?
- How would the equation change if the line passed through different points?
- Can a line have an undefined slope? If so, what does that line look like?
Tip: When solving for the slope, be careful with signs and subtraction, as they can easily affect your final result.
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Math Problem Analysis
Mathematical Concepts
Algebra
Coordinate Geometry
Linear Equations
Formulas
Slope formula: m = (y2 - y1) / (x2 - x1)
Point-slope form: y - y1 = m(x - x1)
Slope-intercept form: y = mx + b
Theorems
Slope-intercept form theorem
Suitable Grade Level
Grades 8-10
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