Math Problem Statement
Which equation represents the line shown in the accompanying diagram?
Solution
To determine which equation represents the line shown in the diagram, let's analyze the graph step-by-step.
Step 1: Determine the Slope
The slope () of a line can be determined by finding the change in over the change in ().
The line intersects the graph at points and :
- From to :
- The rise () is .
- The run () is .
Thus, the slope of the line is:
Step 2: Identify the y-Intercept
The -intercept is the point where the line crosses the -axis. The line crosses at .
Step 3: Write the Equation of the Line
The equation of a line in slope-intercept form is: Where:
- is the slope.
- is the -intercept.
From the graph:
- The slope .
- The y-intercept .
Thus, the equation of the line is:
Step 4: Match with the Given Choices
The choices given are:
None of these match , which is unexpected, indicating I may have missed something.
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Math Problem Analysis
Mathematical Concepts
Algebra
Linear Equations
Graphing
Formulas
Slope formula: (y2 - y1) / (x2 - x1)
Slope-intercept form: y = mx + b
Theorems
Slope-Intercept Theorem
Suitable Grade Level
Grades 8-10