Math Problem Statement
Match each description to the function that models its linear relationship.
Solution
Let's analyze each description and find the corresponding linear equations from the options provided.
Step-by-Step Solution
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First Description: A line goes through points and .
- To find the equation, we need to calculate the slope () using the formula: Substituting and :
- Now, use the point-slope form of the line equation: Substitute and : Simplifying further:
- So, the equation for this line is:
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Second Description: The table with points and .
- Calculate the slope using the points and :
- Using the point-slope form with : This simplifies to:
- The equation for this line is:
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Third Description: A line has a slope of and a y-intercept of .
- Since the slope and the y-intercept is , the equation in slope-intercept form is:
Matching Equations
Now, let's match each description to the equations:
- First Description (through points and ):
- Second Description (table with points and ):
- Third Description (slope and y-intercept ):
Let me know if you need further details or have any questions!
Here are some related questions for further exploration:
- How do you determine the y-intercept of a line if only two points are given?
- What is the significance of the slope in a linear equation?
- How can you quickly identify if a line is increasing or decreasing?
- How does changing the slope affect the graph of a line?
- What are alternative forms of linear equations, and when are they useful?
Tip: When given two points, always start by finding the slope, then use either point to find the full equation.
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Math Problem Analysis
Mathematical Concepts
Algebra
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
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Suitable Grade Level
Grades 8-10