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

  1. Y-intercept: The graph shows the line crossing the y-axis at y=6y = 6.
  2. Slope: To find the slope, we use two points on the line. Based on the graph:
    • The line passes through (0,6)(0, 6) (the y-intercept) and (4,4)(4, 4).

The slope mm is calculated as: m=y2y1x2x1=4640=24=12m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{4 - 6}{4 - 0} = \frac{-2}{4} = -\frac{1}{2}

Step 2: Formulate the Equation

Using the slope-intercept form y=mx+by = mx + b, where m=12m = -\frac{1}{2} and b=6b = 6, the equation of the line is: y=12x+6y = -\frac{1}{2}x + 6

Step 3: Match with the Answer Choices

The correct answer is:

  • C. y=12x+6y = -\frac{1}{2}x + 6

Would you like further clarification or a breakdown of any steps?

Related Questions

  1. How do you calculate the slope of a line given two points?
  2. What is the significance of the y-intercept in the equation of a line?
  3. How can you determine if two lines are parallel or perpendicular based on their slopes?
  4. How can you convert from slope-intercept form to standard form?
  5. 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