Math Problem Statement
Which equation represents the graph below?
Solution
To identify the equation that represents the graph, let’s analyze the graph and use the slope-intercept form of a linear equation:
The slope-intercept form of a line is: where:
- is the slope of the line,
- is the y-intercept (the point where the line crosses the y-axis).
Step 1: Determine the Y-Intercept
From the graph, the line crosses the y-axis at . Therefore, the y-intercept is 2.
Step 2: Determine the Slope
To find the slope , we can use two points on the line. From observation, two points are:
The slope can be calculated using the formula: Substitute the coordinates:
So, the slope .
Step 3: Write the Equation
With and , the equation of the line is:
Step 4: Match with the Choices
The closest option that matches is:
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Math Problem Analysis
Mathematical Concepts
Algebra
Linear Equations
Slope-Intercept Form
Formulas
y = mx + b
Theorems
Slope-Intercept Form
Suitable Grade Level
Grades 8-10