Math Problem Statement
Identify the slope and y-intercept of the line below (graph provided).
Solution
To determine the slope and y-intercept of the given line from the graph:
Step 1: Identify two points on the line
From the graph:
- One point is (y-intercept).
- Another point is .
Step 2: Calculate the slope
The formula for slope is: Substitute the points and :
So, the slope is .
Step 3: Determine the y-intercept
The y-intercept is the value of where the line crosses the y-axis. From the graph, the line crosses at .
Final Answer:
- Slope ():
- Y-intercept ():
Would you like further clarification or additional examples?
Follow-up Questions:
- Can you calculate the slope using two other points from the graph?
- How would the equation of the line look using the slope-intercept form ?
- What does the negative slope tell you about the direction of the line?
- How can you verify the slope using the rise over run method directly from the graph?
- If the line extended, at what x-coordinate would (the x-intercept)?
Tip:
Always double-check the rise (change in ) and run (change in ) directly from the graph to ensure the slope is accurate.
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Math Problem Analysis
Mathematical Concepts
Slope and Y-intercept
Linear Equations
Graphing
Formulas
Slope formula: m = (y2 - y1) / (x2 - x1)
Theorems
Slope-Intercept Form: y = mx + b
Suitable Grade Level
Grades 6-8