Math Problem Statement
Solution
The question asks for the equation of the line that passes through the points and . Let's solve it step by step.
Step 1: Calculate the slope () of the line
The slope formula is: Substitute and :
Step 2: Use the point-slope form of a line
The point-slope form of a line is: Substitute and one of the points, say , into the formula: Simplify:
Step 3: Write the equation in slope-intercept form
Simplify further to get:
Final Answer:
The equation of the line is:
Would you like a detailed explanation for any of the steps?
Here are 5 related questions to expand your understanding:
- How do you find the slope of a vertical line?
- What is the equation of a line that passes through two points with the same -coordinate?
- How can you convert an equation in point-slope form to standard form?
- What is the geometric interpretation of the slope of a line?
- How would the equation change if one of the points were shifted?
Tip:
When solving for the equation of a line, double-check your slope calculation—it determines the steepness of the line!
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Math Problem Analysis
Mathematical Concepts
Linear Equations
Slope-Intercept Form
Point-Slope Form
Formulas
Slope formula: m = (y2 - y1) / (x2 - x1)
Point-slope form: y - y1 = m(x - x1)
Slope-intercept form: y = mx + b
Theorems
Equation of a Line Theorem
Suitable Grade Level
Grades 8-10
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