Math Problem Statement
Write an equation of the line that passes through the given points. (-1,5) and (2,2)
Solution
To find the equation of the line passing through the points and , we will use the slope-intercept form of a line, , where is the slope and is the y-intercept.
Step 1: Find the slope ()
The slope is calculated using the formula: Substituting the given points and :
Step 2: Use the point-slope form
The point-slope form of a line is: Choose one of the points, for example, , and substitute , , and : Simplify:
Final Equation:
The equation of the line is:
Verification with the second point
Substitute into : This satisfies the point .
Let me know if you would like further clarifications! Here are some follow-up questions:
- How do you calculate the slope if two points are given?
- What is the point-slope form of a line, and how does it relate to slope-intercept form?
- Can you derive the line equation if given only one point and the slope?
- What happens to the equation if the slope is zero or undefined?
- How can we find the intersection point of two lines from their equations?
Tip: Always check the equation by substituting the points to ensure accuracy.
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Math Problem Analysis
Mathematical Concepts
Algebra
Linear Equations
Coordinate Geometry
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
Suitable Grade Level
Grades 8-10
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