Math Problem Statement
Find the equation of the line that passes through the points (2, 5) and (−3, 6).
Put the equation of the line in the form y = mx + b and then enter the values of m and b into the answer box below (in that order), separated with a comma.
Solution
To find the equation of the line that passes through two points and , we'll use the slope-intercept form of a line:
Step 1: Find the slope .
The slope formula between two points and is:
Substitute the given points and :
Step 2: Use the slope to find the y-intercept .
We now substitute the slope and one of the points into the equation to solve for . Let's use the point :
Simplify and solve for :
Step 3: Write the equation of the line.
Now that we have and , the equation of the line is:
Thus, the values of and are:
The final answer is:
Would you like further clarification on any step?
Here are 5 follow-up questions:
- How do you calculate the slope between any two points?
- Why is the slope negative in this case?
- What happens if the slope of a line is zero?
- How does changing the slope affect the steepness of a line?
- Can a line have the same slope but different intercepts?
Tip: Always choose points that are easy to work with when plugging into the slope-intercept formula.
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Math Problem Analysis
Mathematical Concepts
Algebra
Linear Equations
Coordinate Geometry
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
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