Math Problem Statement
Which of the following equations corresponds to the graph below?
Solution
To solve this problem, we need to find the equation of the line represented in the graph. Let's go through it step-by-step.
Step 1: Identify the Slope and Y-Intercept
- Y-intercept: The graph shows the line crossing the y-axis at .
- Slope: To find the slope, we use two points on the line. Based on the graph:
- The line passes through (the y-intercept) and .
The slope is calculated as:
Step 2: Formulate the Equation
Using the slope-intercept form , where and , the equation of the line is:
Step 3: Match with the Answer Choices
The correct answer is:
- C.
Would you like further clarification or a breakdown of any steps?
Related Questions
- How do you calculate the slope of a line given two points?
- What is the significance of the y-intercept in the equation of a line?
- How can you determine if two lines are parallel or perpendicular based on their slopes?
- How can you convert from slope-intercept form to standard form?
- What other forms of linear equations can represent the same line?
Tip: To quickly find the slope on a graph, choose two points, count the "rise" and "run" between them, then simplify the fraction.
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Math Problem Analysis
Mathematical Concepts
Algebra
Linear Equations
Graphing
Formulas
Slope formula: m = (y2 - y1) / (x2 - x1)
Slope-intercept form: y = mx + b
Theorems
Slope-intercept form of a line
Suitable Grade Level
Grades 8-10