Math Problem Statement
Solution
To find the equation of the line represented in the graph, we use the slope-intercept form of a line:
where:
- is the slope of the line.
- is the -intercept (the point where the line crosses the -axis).
Step 1: Find the slope ()
The slope is given by:
From the graph:
- The line passes through the points and .
- Calculate the slope between these two points:
Thus, the slope .
Step 2: Find the -intercept ()
The -intercept is the point where . From the graph, we observe that:
Step 3: Write the equation
Substitute the values of and into the slope-intercept form:
Final Answer:
Would you like me to verify this equation or explain any part in more detail?
Related Questions:
- How do you calculate the slope if you are given two points?
- What is the general form of a linear equation, and how is it different from slope-intercept form?
- How can you identify the slope and -intercept directly from a graph?
- How do you convert the slope-intercept form into standard form?
- Can you explain how the slope relates to the steepness of the line?
Tip: Always double-check that the line passes through known points after calculating the equation.
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Math Problem Analysis
Mathematical Concepts
Linear Equations
Slope-Intercept Form
Graphing Lines
Formulas
Slope formula: m = (y2 - y1) / (x2 - x1)
Slope-intercept form: y = mx + b
Theorems
Slope of a line between two points
Suitable Grade Level
Grades 8-10
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