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

The slope $m$ is calculated as: $m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{4 - 6}{4 - 0} = \frac{-2}{4} = -\frac{1}{2}$

Step 2: Formulate the Equation

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

Step 3: Match with the Answer Choices

The correct answer is:

• C. $y = -\frac{1}{2}x + 6$

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.