Math Problem Statement
What is the slope of the line that passes through the points left parenthesis, 4, comma, minus, 6, right parenthesis(4,−6) and left parenthesis, minus, 2, comma, 3, right parenthesis(−2,3)? Write your answer in simplest form.
Solution
To find the slope of the line passing through two points, we use the slope formula:
Given the points and , we can assign:
- ,
- ,
Now, substitute these values into the formula:
So, the slope of the line is:
Would you like more details or have any questions?
Here are five related questions for practice:
- What is the slope of a line passing through the points and ?
- How do you interpret the slope of in the context of this line?
- If the slope is positive, what does that tell you about the direction of the line?
- How do you find the y-intercept of a line given its slope and a point?
- Can two points define more than one unique line? Why or why not?
Tip: The slope of a line indicates its steepness and direction—positive slopes go upward, negative slopes go downward.
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Math Problem Analysis
Mathematical Concepts
Algebra
Coordinate Geometry
Slopes of Lines
Formulas
Slope formula: m = (y2 - y1) / (x2 - x1)
Theorems
Linear Equation Properties
Slope-Intercept Form
Suitable Grade Level
Grades 8-10
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