Math Problem Statement
Solution
To find the equation of a line passing through the points and in slope-intercept form, , we first need to determine the slope and then the y-intercept .
Step 1: Calculate the Slope
The formula for the slope between two points and is:
For the points and :
Step 2: Substitute a Point to Find
Now that we know , we can use one of the points to find . Let's use :
Step 3: Write the Equation
With and , the equation of the line is:
Conclusion
The correct answer is the first option: .
Would you like further details on the steps, or do you have any questions?
Here are some related questions for further practice:
- How do you determine the slope of a line given two points?
- How do you convert a point-slope form equation to slope-intercept form?
- What is the difference between slope-intercept form and point-slope form?
- How do you find the equation of a line parallel to a given line?
- How do you find the equation of a line perpendicular to a given line?
Tip: When given two points, always start by calculating the slope. It helps set the foundation for finding the equation of the line.
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Math Problem Analysis
Mathematical Concepts
Algebra
Linear Equations
Slope-Intercept Form
Formulas
Slope formula m = (y2 - y1) / (x2 - x1)
Slope-intercept form y = mx + b
Theorems
Slope and y-intercept of a line
Suitable Grade Level
Grade 8