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: y=mx+by = mx + b where:

  • mm is the slope of the line,
  • bb 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 y=2y = 2. Therefore, the y-intercept bb is 2.

Step 2: Determine the Slope

To find the slope mm, we can use two points on the line. From observation, two points are:

  • (2,4)(-2, 4)
  • (0,2)(0, 2)

The slope mm can be calculated using the formula: m=y2y1x2x1m = \frac{y_2 - y_1}{x_2 - x_1} Substitute the coordinates: m=240(2)=22=1m = \frac{2 - 4}{0 - (-2)} = \frac{-2}{2} = -1

So, the slope m=1m = -1.

Step 3: Write the Equation

With m=1m = -1 and b=2b = 2, the equation of the line is: y=x+2y = -x + 2

Step 4: Match with the Choices

The closest option that matches y=x+2y = -x + 2 is: y=3x+2y = -3x + 2

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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