Math Problem Statement
Solution
Let's analyze the graph to determine the equation of the line.
The line appears to be straight, meaning the equation will be of the form , where:
- is the slope.
- is the y-intercept (the value where the line crosses the y-axis).
Step 1: Identify the y-intercept
From the graph, we can see that the line crosses the y-axis at . Therefore, .
Step 2: Determine the slope
To calculate the slope , we use two points on the line. The graph shows the line passing through the points and .
The formula for slope is:
Substitute the points and :
Thus, the slope is .
Step 3: Write the equation
Now that we have and , the equation of the line is:
Conclusion:
The correct answer is , which matches the first option.
Would you like further details or have any questions?
Here are 5 related questions for further practice:
- How do you determine the slope of a line from a graph?
- What is the significance of the y-intercept in the equation of a line?
- How would the equation change if the line had a negative slope?
- How can you verify if a point lies on a given line?
- What happens to the equation if the line shifts vertically?
Tip: Always check at least two points on the graph to ensure the accuracy of the slope calculation.
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Math Problem Analysis
Mathematical Concepts
Linear Equations
Graphing
Formulas
Slope Formula: m = (y2 - y1) / (x2 - x1)
Slope-Intercept Form: y = mx + b
Theorems
Slope-Intercept Theorem
Suitable Grade Level
Grades 8-10