Math Problem Statement
What is the slope of the line graphed above? Give your answer as a reduced fraction. Identify the y-intercept. Write it as a point. Write an equation for the line in slope-intercept form.
Solution
Let's solve the problem step by step based on the given graph:
1. Find the Slope
The slope () of a line is calculated as:
Looking at the graph:
- Take two clear points on the line, e.g., and .
- Calculate the rise (change in ): .
- Calculate the run (change in ): .
Thus, the slope is:
2. Identify the y-Intercept
The -intercept () is the point where the line crosses the -axis. From the graph, the line crosses the -axis at . Therefore, the -intercept is:
3. Write the Equation of the Line
The slope-intercept form of a line is:
Substitute and :
Final Answers:
- Slope:
- y-Intercept:
- Equation:
Would you like further explanation on any of these steps? Here are some related questions to explore:
- What does a slope of signify geometrically?
- How do you calculate slope with negative coordinates?
- Can you identify other points on this line using its equation?
- How does changing the -intercept affect the graph?
- What happens to the equation if the slope is steeper (e.g., )?
Tip: Always verify your slope and intercept by checking with at least two points from the graph!
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Math Problem Analysis
Mathematical Concepts
Slope
Y-Intercept
Linear Equations
Formulas
Slope formula: m = (y2 - y1) / (x2 - x1)
Slope-intercept form: y = mx + b
Theorems
Properties of linear equations
Suitable Grade Level
Grades 7-10